0th Day is a glitch which changes the time to 5:59 AM on Day 0. Because it is not supposed to be Day 0 during normal gameplay, this glitch has various effects which are related to which day it is. This glitch is not possible on the Japanese version because you cannot save at owl statues.
This glitch has various effects in different areas, which can include vanishing actors. Most notably, when used in Romani Ranch, the Aliens will be defeated instantly, so you can obtain Romani's Mask without shooting any aliens or having a bow.
The following video documents most of the changes which occur when you activate 0th Day in different areas.
When you select "Yes" on the stored Song of Time text box, your current file's save information will be copied elsewhere. After 41 frames, it will be copied back. This can be used for various tricks and glitches, because the game is partially reverted to the state it was at when you saved.
If you activate 0th Day and then switch mask forms quickly, the C buttons’ dimmed state, which depend on the form after the switch, will not be updated even if items are swapped out. This lets you equip any item over the undimmed buttons and use them.
As an example, at 1:28 on the video above, only C-Right is dimmed because it contains Powder Keg and Link is human. After accepting the song storage and turning Goron, all buttons are undimmed and they remain that way regardless of the item equipped because those 3 original items are usable by Goron.
0th Day is also one of the few ways of performing a Goron Missile, as this glitch requires a first person item to be on Goron's hand. Another effect of holding such items is that if Link performs a Goron Pound right after walking into a wall, he sticks onto it and moves upwards.
Goron Missile can give Link massive horizontal and vertical speed, after a goron pound while holding a first person item. The longer he spends off the ground while pounding, the more speed he’ll have aftewards. Other variables that can influence the outcome are the speed pre-pound, the floor's inclination, whether Link was rolling or walking beforehand and during which frame you released A (if pounding while not next to a ledge, otherwise Link will be sent away regardless).
The video below demonstrates the differences between pounding after rolling, on the first frame after walking and on the first frame after backwalking. It also shows a possible Stone Tower Climb and a Woodfall Temple Boss Key Skip.
With Goron Missile, you can perform Grotto and Fairy Fountain Alternate Exits, Lullaby Skip, the Stone Tower Climb and skip every Boss Key. While it is incredibly powerful, its speedrun viability is held back by its exclusivity to the english version of the game and the lengthy setup required (acquire Owl Save Storage + Song of Time Storage).
Currently, the fastest way to achieve the requirements for Goron Missile is to use the Return A method of Owl Save Storage and an item that produces a text box upon being used, as demonstrated on this video.
Warning: on N64 the game may crash due to Goron having 1st person items on hand, going in first person with them can also be problematic on Wii VC. This video has some more details.
Other ways of achieving a Goron Missile are the use of the minigame state, in order to use 1st person items on B, and Light Node SRM.
This trick notably allows Deku to shoot arrows utilizing any Elemental Arrow (Fire, Ice or Light), with Magic Power acting as ammo, instead of Bow and Arrows. If one attempts to use an Elemental Arrow while having less Magic Power than required by it, but still greater than zero, regular arrows will be shot instead.
To unfreeze Goht without a Bow, transform into Deku Link after activating 0th Day and equip Fire Arrow on an undimmed button.
Likewise, you can shoot Light Arrows without a Bow using the same principle as long as you have at least 4 units of Magic Power. This can be used to shoot through the floor as Deku and Invert Stone Tower.
It is worth noting that if you're playing on a N64 release, you should quickly swap the Light Arrow over a slot usable by Deku right before accepting the stored Song of Time and transforming. Not only because it's faster, but also because pausing after turning Deku may crash the game. This is not an issue on Wii VC.
Simply having Hookshot or Bow on Goron's hand allows you to automatically Action Swap when attempting to use other items. To use these items in the first place, you have to press their respective button to put the item on Goron's hand, curl, then use the item (be sure to target before using the item, the game will crash if you aim in first person). Finally, use the item of your choice for Action Swap! You need to pick up arrows and have ammo for the item you are trying to Action Swap with.
There are 3 important things you must take into Goht's room before using Goron Action Swap to melt its ice:
You can store a Song of Time either by doing an Ocarina Dive and voiding out before the "Yes/No" text box comes up or by doing time stop in front of a Gossip Stone, then playing Song of Time and moving into a load zone before the text appears.
In order to maintain this property, you must not Interact with anything that produces a text box, such as NPCs, signs, locked doors, collect items, Stray Fairies, Gold Skulltulas etc.
There are 3 known ways to acquire Owl Save Storage:
In order to maintain this property, you must neither Soar anywhere (Owl Statues or Dungeon Entrances) nor save at owl statues.
"Item Crap" is the popular name of the trick to prevent item ammo counts from being reset upon confirming a Song of Time. In this case, you'll need to do it with Deku Sticks, so you'll equip swap Stick onto a C Button, equip "real" Stick over another button and duplicate a Bottle over the "real" Stick button. If doing it with the ESS method of bottle duping, you'll need to catch something on the bottle that went over "real" Stick after you pick up at least one Stick to have as your ammo. This way, the equip swapped Sticks will not be reset after using a Song of Time. The step by step can be seen on this video.
In order to maintain this property, you must neither equip over your button that contains the Stick ammo nor equip the item pertaining to the inventory slot over which you equip swapped the Sticks.
Once you're at Goht's room with all that, you have to:
Note: if you take over 2 seconds to transform after confirming "Yes", it won't work. In fact, there's 1 frame after these ~2 seconds on which you transform exactly on it, it may cause the game to crash because it mixes up transformations and its models as seen on this video.
Note: the time of day slightly changes the outcome of saying Yes to Song of Time here. If done during day, the Song of Time text will be cleared automatically. However, if done during night time, the Song of Time text will stay up, preventing you from pausing (for the next step). In order to remove this text, you must either press the Ocarina button or catch something in a Bottle (such as Bugs or Fish, which you can bring on a bottle duplicated over any item slot other than the 6 regular bottle slots, since those are not reset by Song of Time). That will bring up its own text, which can be cleared normally.
Note: depending on your current way of playing the game, having one of these 1st person items on Goron's hand may crash the game. Information about which items are safe to use can be found on this video.
If done correctly, Goron will shoot a lit arrow out of the Deku Stick that appeared on his hand while mid air, which will melt Goht's ice as seen on this video.
The 0th Day state restoring effect can allow you to reload your previous entrance instead of a new one, or load the first entrance of the current area.
This is known as a 0th Day Warp, and there are several ways to accomplish it.
0th Day was the original method of getting an item on C with a bottle in the corresponding slot. Equip swap's discovery allowed an easier and more flexible method without 0th day. This is generally used to keep item amounts between cycles, because your item counts don't get reset to 0 if there is a bottle in the corresponding item slot.
Steps to perform (0th Day Method):