The next part of your quest is getting three pearls, and the first is Din's Pearl.
The King of Red Lions
You'll wake up at Windfall Island on a talking boat, the King of Red Lions. He will tell you how you need to save your sister (and the world), and that you should depart, but he has no sail, and you must get one. Turn left and head up the island. There are a few side-quests you can do here, but if you are just interested in getting the sail, head through the stone arches by the docks at the opposite side. Follow the road until you see a man in a parka behind a counter. If you have 80 rupees, talk to him and buy what he sells. If not, head back on the wall behind the man and you'll find a little dock area. Break the pots for some rupees, and if that still isn't enough, go around slashing bushes around the island. When you get 80, buy what he sells - the sail.
If you're worried about the things you have to do later on, find and deal with as many sidequests as you can. What's available is pictograph missions, Miss Marie and the Killer Bees and Tingle which would pay off. You can't get bombs due to expense, trade quests without a delivery bag and lots of rupees, lighting the lighthouse without fire arrows, photo shoots without color and doing many others things without going through the quests early on.
Equip it and head back to the King of Red Lions. He will explain how to sail, so do so, and head to the next island, Dragon Roost Island. Follow the wind towards the large pillar-shaped island on the horizon. Occasionally you may find some rupees atop barrels, but it is mostly a boring, straight ride to Dragon Roost Island.
Dragon Roost Island
The Wind Waker
When you arrive, the King of Red Lions will teach you how to use the Wind Waker, a magical conductor, much like the Ocarina from Ocarina of Time. Head left and you'll see some blue bomb flowers. Use them to blow up the rocks that block your path. When you reach the top, you'll have to sidle the wall to get across the broken bridge. Drop one more bomb flower and continue on. You'll meet up again with Quill. He'll invite you to enter the island, so do.
The Rito tribe will tell you of their problem with their wing-giving dragon, Valoo, and that he has become violent and angry. They ask you to help Prince Komali, the chieftain's son. Quill will give you a Delivery Bag, for holding letters.
Medli
Take Quill's advice and look for Medli in one of the upper rooms. She'll give you a letter to Komali and she'll also ask you to meet her later. It's not a date. I promise. Head down to the bottom floor and enter the door that doesn't make you leave the area unless you go through an actual door.
In this room, Prince Komali will be sitting in bed holding Din's Pearl, the thing you're after, but you can't get it yet because he won't give it to you. Instead of stealing it from him, leave his room and, in the main room, go through the door with the feathers above it.
Out here, jump down to find Medli. She'll talk to you, and then ask you to throw her up onto a ledge. Pick her up and go to the top of the little hill thing. When the wind blows towards the ledge, throw her towards it and she'll fly up there. She'll give you a bottle for your efforts.
Head over to the center of the room by the rock that has water around it. Equip your bottle and grab some water with it. Climb back up to the entrance to Dragon Roost Cavern and pour the water on the red withered bomb flowers to turn it into one you can use, then throw one down onto the rock below. This will create a lake so that you can swim and follow Medli into Dragon Roost Cavern. Throw bomb flowers into the pots that the statues hold, and they will fall over and make platforms that allow you to cross the lava. The next area is your first sword-equipped dungeon: Dragon Roost Cavern.
Wind's Requiem
You can get the Wind's Requiem by going through the short tunnel and swim to where the stones are. That way you don't have to go to the same place later on. The Wind Requiem can change wind direction and is important for acquiring Triforce Charts which is need to decipher from Tingle. Also noting Cyclos is what you have to look out for. It's a cyclone with a much powerful gusts of wind. You need the arrows to acquire the teleporter to save you from sailing one end to the other end.