I mean, it's called Ocarina of Time, so I can imagine you're excited to discover when and how you get your first Ocarina in the game, right? I would imagine you've seen the video of Eiji Aonuma blowing into the optional Ocarina you can buy with the game, and now you want to dive in and play Saria's Song and Zelda's Lullaby as though you've been playing the Ocarina your entire life.
It might be called 'Ocarina of Time', but you don't actually get the Ocarina of Time just yet.
Once you defeat Queen Gohma inside the Great Deku Tree and land back in Kokiri Woods, the Great Deku Tree will send you on your way to get the other spiritual stones in order to stop Ganondorf. That requires you leaving Kokiri Forest through the gate at the end of the mysterious little village. It's the gate near the training area which is being guarded by a nameless Kokiri. He always looked like an emo with a big ginger fringe to me, but I doubt Miyamoto had that in mind when he was making Ocarina back in 1998.

If you've tried to go past this brave/annoying/determined guard before completing the Deku Tree Dungeon, then you'll know that he stops you from walking past him by doing some strange sort of sidestep dance. Once the Deku Tree has passed, however (RIP), he lets you through to continue on your adventure.
As you leave Kokiri Forest, you run along the bridge and suddenly slow down as a cutscene kicks in. Saria appears on the bridge behind you and gives you something she's been working on for you - the Fairy Ocarina. You'll eventually use this to play Saria's song, a tune you can play to get advice from Saria no matter where you are. She says that she's just your friend, but I've always assumed there's a bit of something going on between these two. Link just seems to break hearts wherever he goes, which is ironic, as you spend most of the game searching for heart pieces.

As soon as you get the Fairy Ocarina, you can carry on into Hyrule Field to continue on with your journey. It's as simple as that - the Fairy Ocarina comes to you after you complete the Deku Tree and leave Kokiri Forest. There's no special task to do, and it's an integral part of the game.

You'll use this Ocarina to change night to day, learn Zelda's Lullaby, play Epona's song, and much more. Eventually, you'll replace it for the Ocarina of Time, the Ocarina that you'll need to open up the door to the sacred realm in the Temple of Time, but you've got a few bosses to defeat before you get that far (including getting annoyed with Princess Ruto in Jabu Jabu's belly!