For most major (and some minor) in-engine cutscenes, the game keeps track of how far you are into the cutscene with a set of bits in the temporary flags region.
By speaking with an NPC in a "broken cutscene" state, this location in memory is still filled in as before. However, the player has control in most cases and is not forced to progress through all of the dialogue box sets. Having this memory partially filled can result in some oddities when bringing this memory state to other NPCs and cutscenes.
Specifics of each use will depend on the number of times the NPC is spoken to, as the values required differ for each effect.
It is worth noting some actions can clear Text Displacement, more of which are covered in the notes further down.
The relevant bytes in memory associated with this glitch are (numbered 1 to 9):
Normally, most in-game cutscenes and NPC dialogues fill out the bits above in order, from left to right. When it is finished it clears the bits. However, leaving during a broken-dialogue state won't actually clear them, thus the "value" of the text dialog box has been displaced.
Now there are instances in the game such as the Gor Coron sumo hall which fill these bits out in an unusual order. Under regular non-glitched circumstances, entering the sumo hall for the first time sets the last four bits at 80406F9D, or bits (6) to (9). Saying "Yes" to start the sumo fight sets the sixth bit at 80406F98, the (1) bit. If Link wins the sumo fight, the game will set the seventh and eighth bits at 80406F98, the (2) and (3) bits, and then the game will proceed with Gor Coron finishing his dialogue.
However if the game sees that either of these final two bits, the seventh and eighth bits at 80406F98, are already set, then it will assume Link has already won the sumo fight and Goron Mines will be accessible, even in the broken Early Master Sword state. We can achieve this by manipulating the TD bits with dialogue and set at least the seventh bit at 80406F98.
For ease of reference, the rest of the page refers to bits as the following:
(The bits afterward in 80406F99 don't necessarily matter and are used for dialogue progression.)
Jacquaid has a spreadsheet of TD sources: here
(See above section for technical details.)
By setting either the second bit or third bit of Text Displacement, then going to the top of Death Mountain and speaking with Gor Coron with the Master Sword obtained, the game will give the textboxes associated with Gor Coron being defeated in the sumo event. As a result, the events afterward associated with his defeat play out - the elevator shortcut is opened on top and the wall blocking Goron Mines is removed. While the Gorons blocking entry to the dungeon do not visibly move until the room is reloaded, it is possible to roll past them to enter the dungeon after speaking to Gor Coron but without reloading the room.
As a reminder, as the title screen cannot be viewed after obtaining Text Displacement and the Spinner is not yet obtained, Early Elevator cannot be used to reach the top of Death Mountain until after displacing Gor Coron's text.
It is important to note that some actions will clear the memory region associated with this glitch, commonly referred to as "eating" TD. This section covers what may or may not allow the player to keep TD. Jacquaid's spreadsheet covers some of them, but the list is not fully complete.
Here is a (non-exhaustive) list of what clears TD:
Here is a (n/e) list of what does not clear TD:
After performing Back in Time, talking to Bo anywhere from 2-6 times will set Text Displacement. (Note: this does not work without BiT or already having obtained the Iron Boots.)
For Goron Mines entry without spinner, it is best to talk to Bo 4-6 times, which will furthest advance Gor Coron's text. [Video WIP]
With a 1-frame Ooccoo pull, Link can warp out of the area before Coro's next dialogue line begins after the bottle text. This sets the second TD bit. The frame for pulling Ooccoo is 9 frames after closing the second bottle text box. This can be timed with a visual cue or using two adjacent beats of a metronome at 200bpm.
After beating Snowpeak Ruins, talking to Rusl at least twice just outside his cutscene trigger will set Text Displacement.
Talk to Louise from very close to her and slightly on her left so that her meowing cutscene pushes Link into Telma's cutscene trigger, deactivating it. She can now receive Renado's Letter, and talking to her will give Text Displacement. (Giving Renado's Letter will not give Text Displacement.)
This method hard to do consistently, but the trick is precise enough and and the cutscene skip by itself saves little enough time (~6s) that spending time setting it up isn't very worthwhile.
On the Wii version, the cutscene trigger for Telma cutscene is smaller, so there's enough room to talk to Telma outside of it. Talking to Telma twice or thrice will grant Text Displacement. (You can also do the same for Renado's Letter.) The region to talk to Telma is not precise and considered to be more lenient.
By pressing A to talk to Yeta and bringing up the map on the same frame, you can roll away after the map closes and before she continues talking to you. This will grant TD.
Note: this needs to be done the first time talking to Yeta in Snowpeak Ruins, as only this instance will set the relevant bits.
By setting the first bit of Text Displacement, then going to Jovani's House and speaking with Jovani with at least 20 Poe Souls obtained, the cutscene where Jovani gives Link the bottle of Great Fairy Tears is skipped entirely (the game progresses as though the bottle were already obtained) and the bottle is rendered permanently Lost Forever.
HD note: A partial fix was implemented for this in TPHD, where the first bit is force-unset before the cutscene triggers, thus awarding the bottle even if Text Displacement was obtained. However, the Poe Lantern, which uses the second bit, was not protected and thus can be rendered Lost Forever if the Jovani Cutscene is viewed with Text Displacement obtained at least twice.
The first time the player warps out of a dungeon with Ooccoo, there is extra text introducing Ooccoo Jr. to the player for the first time. This text changes the TD value. If the player then takes damage and dies while pulling Ooccoo Sr., the warp text will appear while Link has 0 health. Doing this while warping away with Ooccoo Sr. will cause Link to die before the introduction text plays, granting TD. The player can then modify the TD value by pulling Ooccoo Sr. again.
This only works with Ooccoo Sr., and on the first time ever warping out, since that is the only time the introduction text plays.
(Note: Pulling Ooccoo Sr. again immediately after dying then reviving to set up TD will softlock. The player must either die or enter a load zone to avoid this. It also does not matter if the player has a bottled fairy.)