After Navi wakes you, go outside and watch the scene. Head down and talk to Saria.
To get to the next part of the game, you will need to acquire a sword and shield. There is a sword hidden in the forest that you can get for free, but you will need to have 40 rupees to buy a shield.
Get a Sword
Walk to the end of the path leading to your house, then make a left. Walk along the path and you'll see a slope to your left; go up it. Go through the fence maze (or just climb over the fences) and crawl into the hole in the wall. Go through to the end.
Face left and watch for the rolling boulder. When it passes, run and follow behind it, and when there's a gap in the wall to the right, go in and you'll see a big chest. Open it to find the Kokiri Sword. Be sure to equip it. Now turn around and watch for the boulder again. When you see it, follow behind it again. Once you turn the corner and the boulder is out of the way, you'll see a blue (five-piece) rupee next to a bush. Get it. Crawl back out the hole you came in through.
Get a Shield
Now you need to get some rupees. There are several blue rupees scattered about the forest; I will tell you where to find them. You can also cut bushes or run through tall grass to find green rupees. When you have 40 rupees, you're ready to move on.
In the fence maze are a couple of signposts. Z-Target the farthest one (read it for an explanation of how to cut the sign down) and, while holding forward on the control stick, swing your sword. You should execute a stab, which will take the whole sign down. If you only cut part of the sign off, you did it wrong. If you got it right, you get five rupees.
Now go down the slope that took you up to this hill, and go into the house straight ahead. Open every chest for 11 rupees, and a recovery heart. Exit the house, and climb up the ledge behind the house and walk in the narrow passage here for five rupees.
Drop back down. In the water near the house you were just in, there are three stepping stones. Jump across each one (when you run over an edge, you jump automatically) and when you reach the last one, you get a blue rupee. Now you're near the shop. Go into it (you can ignore the girl who calls to you), then go back out. Jump across the stepping stones again for another five rupees. Go back into the house where you opened the chests, then go back out and jump across the stepping stones one last time. Now you should have at least 40 rupees.
Go back into the shop, talk to the shopkeeper, and buy the deku shield. Equip it right away, then exit the shop.
Go to the Deku Tree
To your left is some water; get across it to the arch in the wall on the other side. Talk to Mido (the guy blocking it), and if you have the sword and shield, he lets you pass. Follow the path and eventually some Deku Babas will come out of the ground. Z-target and swing your sword to cut them down. They leave behind Deku Sticks. You'll need these later.
After clearing the Deku Babas out of the way, continue on the path until the scene with the Deku Tree starts. The Deku Tree must test your courage; he has been cursed, and he asks you to break the curse. Say yes, then go into the Tree.