After you get the Earth Element from the first dungeon, there is much to do in Hyrule.
Talk to the Elder
After you complete the first dungeon, if you haven't already, go south from Deepwood Shrine to return to the Minish Village, then go to the northwest house and talk to the Elder, who opens a path for you. Go through the door that he opens.
Your next destination is Mount Crenel to meet Melari, but there are some things to do along the way.
Get Bombs
After you leave the Minish Village, go west through the log. Ignore the sparkling portal and instead go into the little orange house to the north. Talk to the Minish to get a Bomb Bag and some Bombs.
Reveal a Symbol in the Minish Woods
Exit the Minish house and go south to the sparkling portal. Stand near it and press R to return to normal size. Go north and check on the gravestone. It will disappear and reveal a symbol on the ground. You can't use it right now, but it will be useful later.
Get Mysterious Shells
Go west. You can optionally go north to see three Minish doors, but there is no way to reach them right now because you won't be able to swim in the water north of the Minish portal.
Go south from the west side of the bridge, then use a bomb on the three cracked stones to get rid of them. Then go south and exit the forest.
You can ignore the mushroom if you wish. It just takes you across the gap, where you can talk to a Minish who doesn't do anything useful yet, and you can bomb some cracked stones.
Go north, then bomb the weird-looking wall and go into the cave to get 20 Mysterious Shells.
Unlock Kinstone Fusion
Outside the cave, go west, then north up the stairs. The Gust Jar works well on the Peahats that are flying around. Go east, then go north to the next area.
Bomb the cracked stones, then go west, then north to reach Hyrule Town.
When you enter town, the Hurdy-Gurdy Man will give you a Kinstones Bag, tell you about Kinstones, and give you a Kinstone piece.
Whenever you see a thought bubble over a person or object, you can press L to try to fuse Kinstones with them. It takes a moment for the thought bubble to appear. After you press L, you can look through your Kinstone pieces to see if you have a matching one. If you fuse a Kinstone, it will turn into a spark and will travel to some place in Hyrule, and something will happen. Sometimes a chest will appear somewhere, sometimes a path will be opened, a person might get an idea causing something in the game to change, or a special monster may appear.
When you are Minish-sized, there is a chance to find animals that you can fuse Kinstones with.
Be sure to cut grass and bushes for a chance to find green Kinstone pieces. Blue and Red Kinstone pieces can't be found in grass and bushes, and are usually found in chests.
For a full list, see the Kinstone Fusion page. Most of the early Kinstone Fusions are random, and can be done with most people in Hyrule Town, as well as with any Minish. Fusion opportunities may change whenever you enter or exit a building go to a different area.
Fuse Kinstones with the Hurdy-Gurdy Man
If you haven't already, press L in front of the Hurdy-Gurdy man and fuse the piece he gave you with his. It will open a hole in a tree in South Hyrule Field.
Optional: Buy the Bigger Wallet
You can only carry up to 100 rupees right now. If you have at least 80 rupees, buy the bigger wallet from Stockwell's shop (the building with rupees on the roof). It lets you carry up to 300 rupees. If you're close to 80 rupees, it's worthwhile to try to find rupees until you can afford the big wallet. One way to get rupees is to play the Cucco Catching Game, explained later on this page.
After you buy it and leave the store, Stockwell will start selling the boomerang. It costs 300 rupees. If you buy that, Stockwell sells a bigger bomb bag for 600 rupees, but you will need to find the biggest wallet before you can afford it. The biggest wallet will be available later.
Vacuum the Dust
In the town square of Hyrule Town, the southeast rug has dust all over it. Use the Gust Jar to clean it up. Later in the game, a new shop will appear there.
Get a Piece of Heart
Go south from Hyrule Town and go to the southeast part of the area, and go into the open tree (which you just opened with the Kinstone fusion). Take the Piece of Heart, then go back outside.
Reveal a Symbol North of Link's House
Go north past Link's house, then look for another gravestone just north of Link's house. Check on it to reveal another symbol.
Train with Swiftblade
Go back to Hyrule Town, and go west from the entrance to find a log cabin. Go inside and talk to Swiftblade. Train with him to learn your first sword technique, the Spin Attack. Hold the sword button to complete the training and get a Tiger Scroll. You can read it in the pause menu to review the technique.
Fuse Kinstones with Mayor Hagen
Go into Mayor Hagen's house in the northeast part of Hyrule Town, then exit through the east door. Go down the ladder and open the chest for a red Kinstone piece. Then go back to Mayor Hagen and press L to fuse Kinstones with him. This drains a pool in Lon Lon Ranch, but you won't be able to reach it until later.
Reveal a Symbol in Hyrule Town
To the right of the north exit of Hyrule Town, there is another gravestone. Check on it to reveal a symbol.
Optional: Play the Cucco Catching Game
In the southeast corner of Hyrule Town, you find Anju standing outside of her cucco pen. You can talk to her to play the cucco catching game to win Mysterious Shells and rupees. Each time you play, it will be more challenging. However, you can't beat the last few rounds equipped as you are now.
During the Cucco Catching game, press R to pick up the cuccos. While walking around, you can press R repeatedly to roll, which is quicker than walking. If you're having trouble finding the cuccos before time runs out, try to just go around and memorize the locations of the cuccos, then go into a building to quit that round so you can try again. You don't have to catch gold cuccos. They are harder to catch because they will fly out of your hands after a moment, but you can try to throw them ahead of you before they have a chance to fly away, then roll toward them to pick them up again. To avoid making a cucco bounce off of the fence when you try to throw it in, stand to the north of the pen when you throw the cucco in.
Moving On
When you're ready go move on, make sure that you have learned the Spin Attack from Swiftblade in the log house west of the southern entrance of Hyrule Town. Then, make sure that you have at least 20 rupees, and talk to the soldier at the northwest exit of Hyrule Town. Demonstrate the Spin Attack for him, and he will let you pass. Go through and you can make your way to Mount Crenel.