Here is a short (read: crappy) Overworld walkthrough for Legend of Zelda: A Link to the Past. This walkthrough is divided up into two sections, Light and Dark World. Boss strategies are explained here.

Hyrule Castle to Eastern Palace
First thing you want to do is grab the Lantern out of the chest. Now head north to the Castle. When you get to the drawbridge head right and follow the path. Grab the bush to open the secret passage and find your dying Uncle inside. Get your new sword and shield and follow the passage into the Castle. Go through the main doors then left, up, and left to the dungeon. Traverse the dungeon receiving the boomerang along the way, and find Zelda. To take out the guard at her cell toss a pot at it. Now return to the Castle and go up the stairs to the Throne Room where you'll find a secret passage that eventually leads to a room with two levers. Pull the one on the left and go in the now-opened door to the Sanctuary. Meet the Sage, grab the Heart Container and then use your map to head to the village. Some stuff you need to do here is talk to the lady in the house on the hill, plunder her neighbor's house, buy the bottle, and then get the bottle at the Tavern, and get the bug catching net too. Then go talk to the kid that's hanging out at the field, he'll tell you about Sahasarala, so then go after Sahasarala at the Eastern Palace. Head northwest from the ruins and meet up with Sahasarala. Now go in the Eastern Palace (sorry no walkthrough).

The Last Two Pendants
Go back to Sahasarala who will give you some snazzy Pegasus Boots. Head back to the village now. Go to the Library and grab the Book of Mudora. Now head of to the Desert Palace and complete that. Now head off to Lake Hylia. Walk around until you find two caves side by side. Get the Ice Rod out of the left cave and take a walk to that big Monolith. use your new Book of Mudora to read it then move the statues. Clear the Palace and get ready for another trip, to Death Mountain. Go in the cave North of the Sanctuary to get there. Find the Old Man and lead him outside to get the Magic Mirror, this will come in handy. Make you way up to Spectacle Rock, jump off onto the platform you can't see and head into the cave. Get the message from Sahasarala and leave the cave. Head back up the mountain to the transporter and go to the Dark World where you'll become a rabbit. Go up on top of Spectacle Rock and use the Mirror to go back to the Light World. Jump off of Spectacle Rock onto the ledge with Hera's Tower Beat the Tower and get your last Pendant. Now head off to the Lost Woods. Find the 3X3 bush area and cut down the middle bush to enter the Thieves' Hideout. Use the Book of Mudora to read the Pedestal and grab the Sword. Now Head of to Hyrule Castle. Find the double doors with the force field and smash the field with your new sword. Go up the Tower and find Agahnim. He'll send Zelda into the Dark World and disappear. Cut the middle curtain and head onto the Balcony. Beat Agahnim and he'll send you into the Dark World.

You'll arrive at the Pyramid of Power. Grab the heart piece and head off to where the Eastern Palace was. Remember that the Dark World parallels the Light World! Anyhow, go to the place that the Eastern Palace was and enter the Palace of Darkness. Complete it, but make sure you have enough rupees so you can pay off the monkey that lets you in. After beating the Palace you'll get a nice crystal with a... lady inside. Nice. I suggest you use the Magic Mirror to head back to the Light World and grab the flippers from King Zora at Zora's Falls. Now head to the Marsh.

Hammer the stakes then and use the warp to get back to the Dark World. Go in the marsh building and warp back to the Light World, then pull the lever on the right to drain the Marsh. Go back to the Dark World and enter the Palace. Beat it and now head for village. Jump down the well by the Blacksmith's house and toss magic powder in the well to awaken the Mad Bat. He'll make the 1/2 symbol appear over your magic meter and cut your magic costs in HALF. No head for Skeleton Forest and complete the dungeon. Get your third lady-in-a-bottle and your going to have to head for the Village of Outcasts.

There is a pitchfork in the middle of the town. Pull on it to open the door to Blind's Dungeon. You'll find the snazzy Titan's Mitt in this dungeon and battle Blind the Thief (who takes the guise of the girl you have to save!) With Blind behind you you'll want to travel to Lake Hylia. There's a stone there you have to lift that reveals a warp to the Ice Palace. Beat the Palace and grab your fifth lady-in-a-bottle and the Blue Mail.

Now your going to need the Ether Medallion to get into the Misery Mire dungeon. Use the Book of Mudora on a rock that's near Hera's Tower to get it. Use your flute (you got the flute right?) and go to location 6, grab the rock and head to Misery Mire. Beat the dungeon and go to the Death Mountain at the Light World. Find the hill with the three stakes and smash them counter clockwise and jump in the warp that opens. You'll head to Turtle Rock... the last dungeon. Dun, dun, dun.

Beat the dungeon and save Zelda. Now head to Ganon's Tower. This is the time you want to beef up your inventory, I suggest you grab the Golden Sword and Silver Arrows. You'll need the Super Bomb (found at the bomb shop where Link's house was in the Dark World) to blow up a wall in the Pyramid to meet the Fat Fairy. Check the items section for how to get the goods. Now head to Ganon's Tower , which is where Hera's Tower was but in the Dark World. Beat the dungeon (I'll wait 'cause this'll take you A LONG TIME). I'm waiting, go... I said go!

At Agahnim? Good. Beat him and then chase after Ganon. Beat Ganon and head up the new- found stairs. Grab your brand new Triforce of Power and congrats, you stopped Ganon's planned invasion of Hyrule! Pat yourself on the back, you did good.