Let's start with Hyrule, the equivalent of the Overworld from Zelda 1.
There are five sections of Hyrule: Northwest, Central west, Southwest, Northeast, and Southeast.
There are the following types of terrain on the Hyrule map: Road, plain, forest, desert, swamp, graveyard, lava flow.
When Link is walking on the road, he cannot be attacked. When he steps onto another kind of terrain, however, black monsters appear. There are two types of these - weaker ones shaped like Bots, and stronger ones shaped somewhat like Ganon. If Link is hit by either of these, a battle commences. Enemies encountered if Link is struck by a Ganon-monster are tougher. Luckily, the Ganon-monsters are rarer. Occasionally, Faeries will appear. If Link collides with one of them, a fairy that restores his life will appear.
Link will be able to enter several different towns.
The townsfolk come in a small variety of templates. There are women carrying bowls on their head, women with long hair, old women, and men.
Long haired women in blue, old women in red, and men can be seen walking around the town. They generally have nothing important to say, and at no point are they crucial to winning the game.
Long haired women in red will usually refil Link's life meter if he enters their house. Some of them are involved in quests for spells.
Old women in orange will refil Link's magic meter.
Bowl-carrying women in blue and old women in blue are always involved in quests for spells.
Zelda II is the only Zelda game, save the non-canon CDI games, that plays as a side-scroller rather than from an overhead view. Link can stand, duck, and jump roughly his own body height. Link's shield is held at chest height. He must duck to block low-flying projectiles, and to stab shorter enemies. Later in the game, he will learn the Downthrust and the Upthrust.
Aside from the battles that take place on the various types of terrain, there are also caves and palaces.
Unlike other Zelda games, Link does not receive stronger swords, shields, and tunics. His stats increase as he gains experience, as in a traditional RPG.
Link's three stats are Attack, Magic, and Life. They respectively determine how much damage his attacks do, how many magic points his spells cost, and how much damage he takes from enemies. Each starts at level 1, and can be raised up to level 8.
His Life and Magic are measured in "meters". The Life meter is red, the Magic meter is white. Each one is broken into blocks. A single block is 16 hitpoints or magic points.
Link gains experience points (EXP) for defeating enemies. When he reaches a preset amount of experience, he can trade those points in for an upgrade in one stat.
Link starts at the Hyrule Temple in Northwestern Hyrule.
First, go south. You will see a cave. Enter it. Without the Candle, the cave will be dark, but don't worry. Watch the ground. Where it flickers, that is the motion of the enemies in the cave. Duck, and stab, and kill them as they approach. Moving in, you'll find a series of small indentations in the ground. Each one of those has an enemy in it. Kill these, head to the back of the cave, and get the Magic Jar.
Return to the road that lead away from Hyrule Castle. Follow it to the fork and then follow the fork southeast. You will come to the town of Rauru. Here you can refil any damage you've taken, and get the Shield Spell.
To Parapa Palace
Head east from Rauru, bearing north, through the forest. You'll come to a cave. The cave has one Lowder in it. Remember to watch the floor so you can see its foot movements. You'll exit the cave and be in Parapa Desert.
Weaker random encounters in the desert have no enemies, but are full of stones blown by the wind. They do minor damage, but can add up. Head east and then south. You'll come to a long stretch of road. Travelling along it you'll be interrupted by a side-scrolling area that involves jumping across pools of water while dodging bubbles that float up from below the ground. The biggest danger here is to be hit by a bubble after jumping and be knocked into the water.
Across the cliffs, you'll see a small area of forest surrounding a single square of plains. Head to the plains, and you'll again be brought into a side-scrolling area. This one has one Orange Goriya, and a Heart Container. Fighting in the forests nearby can be very dangerous at your low level, but profitable as well. Moblins are worth 20 exp each, but they can kill Link quickly.
Head north to the desert, and keep heading north. Parapa Palace is at the northeastern tip of the desert. Enter it.
To be completed.
The strategy for defeating Ironknuckles is to do one stab standing, one stab ducking. An Ironknuckle will never move its shield if you don't change your attack, and you can't "fool it" by stabbing low repeatedly and then stabbing high. Watch for the sword. Orange Ironknuckles are slow and you can see the stab coming. These guys really aren't that tough, their defense sucks compared to their red and blue bretheren.
Horsehead is kind of a tough boss before you get the hang of fighting him. You'll probably want to have your Attack level at 3 before tackling him. He attacks with a short mace, and his body is armored. His head, with is about a head higher than Link's, is his only vulnerable part. It requires precise timing to hit him. However, hitting Horsehead knocks him back. With the right timing, Link can do a short jump, hit Horsehead, and he'll be knocked back so that his mace swing misses. Repeat, and Link can drop Horsehead in seconds without taking a single hit.
Congratulations, you've just completed your first palace.
Past Horsehead is a turquoise statue. Walk up to it, and one of the six crystals Link carries will be placed in the forehead of the statue. Link's life and magic meters are refilled, and his experience is filled right up to the next level. So you may want to make sure he's just gained a level before doing this.
(Or you can do what I do, and don't put any crystals in until the last minute. See, the game doesn't care whether you need 50 or 8000 EXP for your next level. If you put the crystal in the statue, you get as many EXP as you need. So why not just wait and put the crystals in once you've gotten to the point where each level requires many thousands of EXP?)
Get the Jump Spell
Having defeated Horsehead, go back to the cave you reached Parapa through. Now that you have the candle, it will be lit up and you can see the Lowder. Go back, follow the road north to the other desert. This is the Desert of Tantari. Go north, and there will be a very prominent cave.
Enter it. Fight past an Ache, being careful not to get knocked into the lava, and then kill a few Red Octoroks. Past them is a Red Goriya. The Goriya is guarding a winged orange thing - a Trophy. Kill the Goriya, get the trophy, leave the cave. Go back to the road and take it West. You'll reach a second town, the town of Ruto.
In the town of Ruto, find one of the two long haired women in red. She'll thank you for saving the trophy, and let you into her house. Head to the basement, talk to the Wizard, and get the Jump Spell. You'll need it.
Head south until you come to a cave. You may have been warned not to go south without a candle by one of the random townsfolk... this is why. This cave is long and tough. In the first section, fight past red Octoroks and a Red Goriya. In the second, fight past Lowders and another Red Goriya. Use Shield to get past the Goriyas if you need to, but make sure you have enough magic to cast one shot of Jump. In the final section, you'll be fighting Aches, and your first Acheman. Try to catch him before he lands, if he does land, be ready to jump his fireball.
Central West Hyrule
Once you're out of the cave, there will be no road in sight, but a single square of forest to the right. Go there. There's a hidden fairy there, and you'll probably need it.
This is also the first time you've seen swamps. If Link tries to walk through swampland, his movement speed is cut in half, making it tougher to avoid enemies than usual. And if he gets drawn into battle in the swamp, his speed is also reduced as his boots stick in the muck.
So, stay west and follow the grasslands south. Then cross the swamp at its narrow point and head west. You'll see a road. Get to it.
Before you head for the Town of Saria, head north into the woods. Link will be repeatedly interrupted for side-scrolling battles with Megmats. One square in the forest, nearish the middle, has a house. Enter it and talk to the man inside. His name is Bagu, and you'll need to have talked to him later in the game.
Now, head south. There's a bridge in plain view - you can take it if you want but it's probably not a good idea. The bridge swarms with Bago Bagos. The easier though longer route is southeast through the forest, the small desert, and then across a bridge with Lowders and bubbles instead of Bago Bagos. Soon you'll be in the Town of Saria.
Town of Saria
Remember back at the beginning of the walkthrough when I mentioned the few kinds of townsfolk that are rarely useful? They're downright dangerous here. They can turn into Aches if you talk to them. Town Aches do more damage than regular ones, and some Town Aches have the same hitpoint amount as Bubbles, meaning you'll be stabbing them endlessly to kill them. Did I mention that if you talk to a person, you can't undo the dialog box and the Ache may keep attacking you? Cheap.
Of course, any townsperson who exits a house or who is standing still is safe to talk to. You'll come to a woman in a very big house who complains that she lost her mirror. Go to the next screen, enter the small house. It will be empty. Walk to the table, try to talk to it, and you'll find a mirror under the table. Go back to the woman, she'll let you inside, and a Wizard in the basement teaches you the all-important Life spell.
At this point, you can Sequence Break. Either head for Midoro Palace or south to the Death Mountain Area. Technically, you're supposed to go for the Palace first. If you want to do Death Mountain first, skip to that section.
Route to Midoro Palace
If you want to go for the Palace first, head back the way you came out of town, back across the bridges and get to the road. Head west, and you'll see a boulder blocking the way. You can't break it now, so head north. Eventually you'll see another boulder blocking the way. Now leave the road and head east. Go past the cave (unless you want to fight some enemies and get a P Bag) and you'll be at Midoro Swamp. The road leads through the swamp, but has been broken up. A battle or two is almost unavoidable, but you can make it a little easier on yourself by stepping into the swamp until the enemies appear, then stepping onto the road. Road "battles" have no enemies, and you'll have a bit of time to walk through the swamp before the enemies reappear afterward.
Route to Death Mountain
At the end of town, there will be a river with no bridge across it. Enter the tiny hut near the river's edge and talk to the guy inside. If you spoke to Bagu as I recommended earlier, he'll extend the bridge. If you haven't, he won't. Anyway, cross the river. There's a cave, but if you enter it, you're transported into the Southwest section of Hyrule, aka the Death Mountain Area.
I'll do the walkthrough of the caves later.
The big problem around here is Dairas. Axe-swinging crocodile monsters that you have no effective way to fight. Orange Dairas... there's a sort of rythym you can get into, where you stab the Daira before its axe swing, and the recoil knocks it back so the axe misses. But if you lose the rythym, you will get chopped to bits by the axe. Red Dairas are actually a little bit easier IMO. They throw their axes, do more damage, and have more hitpoints, but their attacks are easier to dodge. Thrown axes can be jumped.
Once you've wound your way through the maze of caves, you'll see an area to your left with a black square in the middle and a boulder next to it. This is Spectacle Rock.
Spectacle Rock of course was the location of Death Mountain/Level 9 in the first Zelda game. Somewhere I read that the black pit was literally what was left of Level 9. I think in some official Nintendo Guide that had the Mario Series, Zelda series, Startropics, and a couple others... it's been a decade and a half since I read that thing, I don't remember what it was called.
Anyway, Spectacle Rock is the only cave with totem statues in it. And it's a doozy. Fight through Red Dairas, Achemans (Achemen?) and Lowders on the first screen. On the second, kill some Megmats, an Orange Daira. There will be an elevator. Ignore it for now and head right. A room with a few Red Octoroks and a red Magic Vial. Don't get the Vial if you don't need it.
Now take the elevator down. More Red Dairas... *sigh*... use Shield Spell if you need it, but if you do, try to get them both killed so you don't waste magic. One Red Daira is to the left up on a raised platform. Try luring him to the edge, then turning and stabbing him on the legs. There'll also be a little critter called a Myu there. Stab it if you can while it's on the platform, because unless you can hit it up there, you can't kill it. The Red Daira to the right is a tough one, because there's no easy way around him.
To the left is a room with Red Octoroks and nothing else. No need to go there unless you want the EXP. Back in the lower elevator room, head right.
This room is a series of pits filled with lava. Jump across them, none of the jumps are tough, but watch out for the Myu. He can knock you into a lava pit. Head right again. On this screen there will be one Orange Daira, one Red Daira. If you're running low on health and life consider running past them, taking a hit or two, otherwise try to kill them. At the right end of the room is the Hammer.
Go back left. Back through the lava pit room, back to the lower elevator room, take the elevator up, head left past the Achemen, and get outta that cave.
Now that you're outside again, head East and take the cave. This one has Red Octoroks and some tricky jumps. Once you're through it, head north and take the cave, which rather than taking you to a battle takes you back to Central West Hyrule and a bridge. The bridge has fights. One against a pair of Moblins and a Lowder, one against a Red Daira with bubbles coming up from below. Consider using the Jump Spell to jump over him and run if you don't feel up to tackling him.
Now you'll be just east of the graveyard. Follow the road north along the edge of the graveyard, being careful not to enter it. The Red Moas in the Graveyard deduct more EXP when they hit you than you get for killing them, and they do a lot of damage and are hard to avoid. And if you get hit by a Ganon enemy in the graveyard, you'll also have Red Dairas to contend with.
Anyway, keep heading North. You'll reach the top of the graveyard. Go north again across a small stretch of desert and you'll see the road and the roadblock you encountered on your way to Midoro, but you're on the far side of it now! And now you can use the hammer to smash the boulder.