Moon jump (MJ) is not a glitch in vanilla Twilight Princess: It is a cheat code that gives Link upward speed when the player presses R + A. This page includes resources for tricks used in moon jump speedrun categories that aren't relevant to speedruns without the cheat code.
This page contains many of the videos on ChrisIsAwesome's playlist, but some videos on the playlist aren't included.
It's important to be familiar with movement speeds for Link's various movement options and long jump attack speeds when deciding how to use moon jump. Full speed LJAs are often the best option when possible, but sometimes setting up for a full speed LJA takes long enough that a sidehop, normal jump attack, or even forward jump ends up faster and/or safer. Enemy LJAs can be worthwhile when the boomerang isn't available. This page generally won't include descriptions of moon jump strategies that are as simple as picking a visual cue.
See this page for detailed information on when Link will take fall damage. This is very important information to be familiar with for moon jump speedruns.
The hidden skill map always contains the collision and load zones for the platforms Link stands on when he enters through the various howling stones in the overworld. With moon jump, it's possible to enter the map with one howling stone, carefully jump to the platform for another howling stone, and exit back to the overworld from the new howling stone. This requires first moon jumping high enough that the golden wolf unloads, which makes it possible to enter first person and line up the jump.
This spreadsheet calculates setups for howling stone alternate exits given the starting coordinates and angle and ending coordinates. The blue rows are the results; e.g. for the alternate exit from Sacred Grove to Snowpeak, the goal angle is 32042, and a way to reach the platform is to B attack (30 speed) and hold moon jump for 19.6 seconds before releasing it, or alternatively to jump attack (26 speed) and hold moon jump for 22.6 seconds before releasing it. These can be timed using your speedrun timer. These setups ideally make Link land in the destination load zone, as landing elsewhere on the platform will deal 4 hearts of fall damage.
Moon jump between Link opening a door in a dungeon and him trying to run forwards to the next room, then release moon jump to allow him to land. (If you don't allow him to land, he'll end up stuck and unable to void out, so you'll need to savewarp.) This leaves Link out of bounds when the new room loads. From here, depending on context, it may be useful to let Link drop into water or moon jump further to land on a higher platform or jumpslash out of bounds or onto the door frame. For example:
MJ interrupts the poe soul ripping animation, allowing Link to warp away before the text comes up. However, it is possible to warp away too early and not get the soul. A good approach is to only go through with the warp if the soul ripping sound effect plays while the map opens, as this means you'll never warp away without the poe soul counting. If the sound effect doesn't play while the map opens, you probably opened the map too early, though there is one frame where choosing to warp will let the sound effect play on the frame between the map closing and the warp beginning, which does count the poe soul. Opening the map on the last possible frame before the poe soul text begins fails to warp and gives Map Glitch instead. There is a 5f window to successfully warp away with the poe soul still counting, including the frame before the sound effect plays but not including the Map Glitch frame.
After moon jumping high up while talking to Midna, Link can fall so quickly that, with the correct spacing, he can ignore floors. Since the spacing depends on the height difference between Link's highest point and the floor, MMD setups usually involve standing in a certain place and releasing moon jump at a specific time, or after a certain time if Link just needs to reach a ceiling. Timing moon jump can be done with cues from the Midna text, the run timer, a metronome, or other things.
This strategy is inconsistent because of the roof's slope.
Jump attack MJ over the load zone; don't go to far or Link will fall back in bounds. Walk to the right side of the far end of the tunnel and aim Link towards the end of the sewers by looking at the minimap. Jump attack to the end.
This LJA needs to be aligned well to load the piece of the map linking Faron Field to the Gorge. It also needs to go high in the air to avoid an invisible wall, so it will deal two hearts of fall damage.
Shown at 39:00.
This can be done even with high water.
It's faster to use the B&C to break the ice if you have it.
Saves ~40s over LJAing to Yeto and then snowboarding with moon jump.
The boomerang appears to go directly away from Link until it reaches the targets, so LJAing on any of these frames (up to 10 or so if you target as high as possible) will give you the same angle, and that angle works. On the frame the boomerang reaches the targets, it changes to an angle that doesn't work, and then starting on the frame after it changes back to the working angle. But LJAing within the first 10 possible frames is easy enough to do consistently.
(I found a couple other setups before this one that involved less rolling, but they had 3-4f windows for LJAing, so this setup sacrifices a second or two to expand the frame window to something very comfortable. I think one of those setups was open door on right side, roll, JA autospin, angle buffer to 577xx, throw rang without targeting.)
Example at 5:32:27.
This can be done on any floor after a fairy floor. f21-f32 is the longest stretch without poes.
This setup takes advantage of Link losing speed midair during a jump when the control stick is neutral to make it so he's moving very slowly by the time he's over top of the next door.
MJ in the narrow gap between the platform and the ceiling.
Getting past the shortcut room gate makes it possible to get the bow and third key shard without fighting Dangoro.
An easier but slightly slower alternative for steps 1-4 is to MJ and grab the gate, pull the item wheel, MJ with the item wheel open (always give 1 frame of MJ after closing the item wheel), then close the item wheel to automatically grab through the stone ceiling (no control stick input required). Then carry on from step 5.
Clawshot onto the medallion and begin moon jumping as Link approaches it. This will make Link ignore the ceiling. Cancel the clawshot when Link is above the room, then jumpslash across to the door.
MJ while Link has turned to look at the door closing behind him, then jump attack out of the cutscene trigger. This skips the long intro cutscene and leaves the door to the bedroom key unlocked. If savewarping from the bedroom key, this skips the entire chilfos fight. If leaving normally after the bedroom key, get the key before killing the final chilfos, then moon jump towards the door during the cutscene of it opening.
Shown at 31:44.
During Midna's last text box before the 1-framer, moon jump all the way to the ceiling with 1 heart or less. Clear the text box, then release moon jump frame perfectly so Link lands and dies on the 1-framer. This skips the cutscene with Yeto and Yeta. One way to time this is to set a metronome at 449bpm, press B on beat 1 to close the text box, and press and hold B again on beat 17 (which is equivalent to beat 9 if counting in twos, or beat 5 if counting in fours) to override the moon jump inputs and fall.
Use door trick with iron boots on to jumpslash onto the door frame out of bounds. Time pressing B and holding L when the door closes. Jumpslashing at the wrong time can make Link fall out of bounds, land on the door frame in bounds and crush void, or land entirely in bounds in the next room.
Like a standard door trick, MJ when Link finishes pushing the door up. However, in this case, MJ can only be active for a maximum of 2 frames before it causes Link to get stuck and forces a savewarp, so this is risky. If successful, jumpslash beneath the room to the boss key, then crush void on top of the torch to respawn outside the boss key room.
Shown at 59:08.
At the lower door from the first room in the east wing, clawshot onto the medallion and begin moon jumping as Link approaches it. This will make Link ignore the ceiling. Cancel the clawshot when Link is above the room, then jumpslash across to Aeralfos.
Shown at 1:38:16
The best way out of the boss key area with the gate down is death warping, so prepare by damaging down. Getting to the boss key with this setup costs 2 hearts.
Shown at 2:09:57
Dry roll and tap right to adjust Link's angle partway through, then sidehop left and tap MJ repeatedly to fit Link into the gap in the wall.
Shown at 2:11:03