It's possible to escape the forest region through the Lost Woods, gaining early access to the rest of the world. See Forest Escape for more information.
Getting off the Lost Woods Bridge allows you to go directly to the Lost Woods without having to waste time taking a detour through Kokiri Forest. The fastest way is to use the Longshot to hook onto the ladder. If you don't have the Longshot, but have Bombs, you can perform a Pressure Jump to hop over the rails.
From the Hyrule Field entrance, you want to get into the corner that forms between the hollowed out tree entrance and the bridge rail on the left side, closest to you, then Z-Target so that your flush with the hollowed out tree. It's easier to get into position if you use rolls and sidehops rather than walking, as Link will tend to do odd small hops in this corner.
Once in position, drop a bomb. The slope of the hollowed tree should push it to the side. Then, around when the bomb begins to flash faster, hold right to cause Link to perform a small jump just as the bomb explodes, pushing Link on top of the railing, allowing you jump down below. With perfect timing, it's possible to completely miss the ledge altogether and land below.
It is also possible to Megaflip or Staircase Hover with only 1 Bomb.
To hookshot to the top of the ladders in the Lost Woods more efficiently, target the right or left (depending on your position) tip of the rail of the ladder and hook on. If you are more towards the left of the ladder, aim at the right rail, else do the opposite. When done perfectly, you should clip behind the ladder, and grab on to the ledge instead.
With hovering, it is possible to hover over the walls around the Lost Woods into an "unloaded" portion of the Lost Woods. If you walk back into the "loaded" portion, you will cause the loaded area to reload, resulting in the duplication of all actors in that section.
This can be used to duplicate the Skull Kid heart piece multiple times. You can also duplicate Gold Skulltulas and the Deku Stick uppgrade to buy it twice
There are multiple ways to skip Mido as Adult. Usually the best one is to Backflip with the Hookshot on the right side of Mido to jump above him. If it doesn't work, try another angle. You can also Backflip without Hookshot but the angle and the position is even more precise.