It is possible to escape the forest before beating the Deku Tree using a number of different methods.
Requires: Kokiri Sword or Deku Stick
Skips: Deku Shield, Fairy Ocarina
Also known as "Aqua Escape", this is one of the easiest methods to escape the forest.
Go through the Lost Woods to the small pond where you can enter Zora's River. Roll from the bank of the pond and grab the top of the gray box. Now wait for the Navi icon to appear. You can time this to correspond with the Lost Woods music like in the video. Now press B twice--once to pull Link back off the box, then a second time to jumpslash. Immediately talk to Navi in order to dive off the text as your jumpslash pulls you back off the ledge.
If you fail the dive, save (if appropriate) and restart the game or else Navi will not appear again for approximately 30 minutes.
This method avoids waiting for Navi to appear, but is somewhat harder to perform.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Obtains: Fairy Ocarina
This method is also commonly referred to as "Pokey Escape", and is one of the most common and simplest methods for escaping the forest. First, head over to the Kokiri that is guarding the exit and cut down the sign next to him. Crouch down parallel to the wall and aim your shield a tad bit to the left. You can also go into first person mode and aim a bit to the left. Typically the jewel of the sword is aligned to one of the green streaks on the wall. Now crouch stab and then quickly press A. You will want to get ISG. If all is done correctly then you should have clipped through the guard.
Now you are inside of his circle, but he is still blocking your way. You can kill him by slowly walking to the left side of the log; he will just fall out of space and you can freely move on. Your other option is to move to a spot in the circle where he no longer says "Speak" on the action icon, and do a well timed roll slightly to one side in order to roll underneath him and escape.
Requires: Deku Nuts
Skips: Kokiri Sword, Deku Shield
Obtains: Fairy Ocarina
While this method is possibly the slowest (since you must obtain the Fairy Ocarina), it is notable as it is the only escape that allows you to skip the Kokiri Sword, Deku Stick and Deku Shield, making it useful for puzzle or challenge runs.
To perform this trick, start by doing the Walking While Talking glitch, using the crawl space near the training area where you get the Kokiri Sword. After exiting the crawl space, quickly read the nearby sign before the camera focus returns to Link. As an alternative, you can instead wait until Navi wants to talk before entering the crawlspace, then after exiting the crawlspace use C-up to talk. Immediately toss a Deku Nut, once the dialog message box pops up.
You should now have a free range of motion, but it will be difficult to get your bearings as the camera will be locked in place. Link will act as if he's targeting an object where you were originally standing, moving in a circular fashion around this spot.
Navigate Link over to the exit guarded by the Kokiri by finding your way through the fence. You can either zig and zag out of the fenced area, or try to jump up on it and get outside of it from the side. Pay attention to the audio, as Link may grab on to a ledge on your way out.
Once you reach the exit, Link will simply leave the forest. The Kokiri kid will not be there as long as the camera is focused near the crawlspace.
Requires: Kokiri Sword or Deku Stick
Skips: Deku Shield
Obtains: Fairy Ocarina
At the small pond in Kokiri with the waterfall, jump onto the middle platform. Face toward where Mido should be and sidehop off toward the waterfall and jumpslash. If you timed it correctly you should ricochet off the platform and splash into the water. Now activate an ESS by holding your joystick slightly up-right. Make sure you keep your joystick in that position! Now ESS over to where the Kokiri guy blocking your way to Hyrule Field and ESS into the corner that's closest to the Kokiri Sword area. If you have enough speed, when you talk to the Kokiri you should glitch through him. When you finish the text, you should now be a bit inside the tunnel. Now just follow the instruction above on getting out of his circle.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Skips: Fairy Ocarina
This was the original method of escaping the forest. First, head to the Business Scrub in the Lost Woods. Activate ISG off the Gossip Stone, and then align slightly to the left. The goal is to sidehop to the left and use the Business Scrub's deku nut attacks to hover in the air. You need to continue doing this along the left side of the wall. After gaining enough height and distance, you must then use the deku nut attack and Megaflip to the Lost Woods bridge.
It is possible to get the same height and distance as in method 1 with fewer nuts. This involves using 3 backflips along the wall, this time angled slightly to the right. After the 3 backflips, you now can Z target the Business Scrub and change your angle, just be careful not to get hit from his deku nuts, or shield them back, killing him. You can roll as they are approaching to usually just break them. You want to change your angle to the same as it was in method one, slightly to the left. At this point, you may need one or two sidehops to the left to gain the last bit of height or distance. Then just megaflip like before to land on the ropes.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Skips: Fairy Ocarina
The fastest way to the Lost Woods bridge is by clipping through it. This means that the height and distance required are significantly lower. It is an extremely precise trick, but is still possible on a console. You want to aim a little further to the left before starting this one. Only two or three sidehops to the left are needed in this case. Then, instead of doing a megaflip, you can do a mega sidehop. You want to aim slightly to the right of the tree. Link will actually clip the bridge from underneath. The position is absolutely key so watch the video and try and replicate it as much as possible.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Skips: Fairy Ocarina
Megaflip straight backwards after a sideroll rather than diagonally, then target the scrub and unsheathe a weapon at the right time to get a boost and clip from under the bridge. Because of the extreme precision necessary to perform this trick, it is considered TAS-Only.