Differences between Wind Waker and Wind Waker HD

This NeoGAF thread and this Zelda Wiki page have a pretty comprehensive list of changes, some of which will defy walkthroughs for the original. These are some of the bigger ones:

• The Swift Sail is a new item that can be obtained from the Windfall Auction. While using it, sailing speed is doubled and the wind is always at your back.
• The Tingle Tuner has been removed. Tingle Statues can now be collected with regular bombs instead of Tingle Bombs.
• Presumably related to the above, the Knuckle figurine is now required in order to complete the Nintendo Gallery (was previously optional).
• Tingle Bottles replace the Tingle Tuner. They can be used to send notes and Pictographs to Miiverse.
• The Picto Box can hold 12 pictos (was 3). Pictos are rated for quality the instant you take them, so you can delete and retake on the spot if it's not accepted.
• The Deluxe Picto Box is earned the instant you complete Lenzo's tasks; you don't have to bring him a Forest Firefly. Doing so just gets you a Joy Pendant.
• Pictographs can be uploaded and downloaded to and from Miiverse. This makes it possible to get pictographs of things you may no longer be able to get in the current file.
• The Deku Leaf has a glowing indicator on the ground to point where you would land if you drop.
• While firing bombs at sea, a line is drawn showing what path the bombs will take.
• Magic Armour now drains your Rupees while in use, instead of your magic.
• Items enemies drop last longer before disappearing.
• Items dropped by enemies at sea will fly towards you with okay accuracy, instead of appearing in a Treasure Sphere.
• Several item-based animations are significantly faster (e.g. Grappling Hook swing point attachment and chest salvage).
• The Wind Waker is always equipped on the D-Pad. While sailing, the Grappling Hook and Bombs are as well (with new icons), while the Sail is always equipped on the A button.
• Hero Mode is an option that can be toggled at any time before loading a file. It doubles damage taken and blocks recovery hearts from appearing.
• Five of the eight Triforce Charts have been deleted and replaced with the actual shards. Therefore, you only have to decipher 3 maps, not 8, saving you 1990 Rupees.
• Five new Treasure Charts have been added (42, 43, 44, 45, 46) to take the place of the removed Triforce Charts; they do not appear to lead to anything special.
• Forest Water lasts for 10 minutes longer (30 instead of 20), making it easier to complete the "water the withered saplings" sidequest.
• After the first time, Fishman advice can be read at any time without having to re-feed them.
• Getting hit while on your boat tends to not knock you into the water most of the time.
• You can change direction while swinging on a rope without having to stop.
• Enemies tend to have less invincibility after getting hit. This makes some swings capable of hitting twice.
• You can move while first-person aiming with several items.
• The "grab" and "climb" buttons for blocks have been merged, so you must walk into blocks for several seconds to climb them (like in the N64 games). This is pretty much a downgrade and a real curious decision.
• Treasure Spheres dropped by enemies will always contains their "spoil" item, should they have one.
• The bottom of the Savage Labyrinth now contains the Hero's Charm, not a Heart Piece. This heart piece is now found with treasure chart #46.

There are a number of changes that were made in Wind Waker HD. For the casual player, playing as intended, the two main differences to consider are the removal of the Tingle Tuner, and the addition of the Swift Sail.

The Swift Sail is an upgrade to the sail that automatically sets the wind direction, and also allows the King of Red Lions to go significantly faster than with the normal sail. The Swift Sail can be found in the Auction House on Windfall Island after beating Dragon Roost Cavern. It's not required, but it makes sailing so much faster and easier.

A change that affects fewer players, the removal of the Tingle Tuner, means just that: you cannot use the Game Boy Advance to assist your gameplay whatsoever (most walkthrough will probably assume that you do not have the equipment to use the Tingle Tuner anyway). The Tingle Statues, however, are still in the game, but Link can now use his own bombs to reveal the chests they are in, instead of needing to use a Tingle Bomb.