Link enters the boss arena whenever he touches the loading zone to it. He does not have to actually open the door. By touching a loading zone from out-of-bounds, it's possible to perform a variety of Boss Key skips. Depending on the dungeon, they can either be done from the very first room (exploiting the property that, as a type of collision, all loading zones in a scene are always loaded), right in front of the boss door itself, or anything in between.
This page will attempt to showcase the most modern setups for each of these Boss Key skips, favoring brevity and modernity over historical preservation, while the dungeon pages will serve the latter purpose. The setups shown here (or something close to them) are what most people should be using in runs.
Woodfall Temple has two main methods to skip the boss key, denoted by the floor of the dungeon they take place on.
Upstairs Boss Key skips, while somewhat slower in isolation, conserve so many explosives that it's almost always the preferred method unless you have chus to burn. These work by hovering up to the pillar (using the Deku flower for a little extra height), grabbing the ledge as Zora, then doing a Zora ledge clip on the left hand side of the pillar. From here, 3 megaflips should be all it takes to touch the loading zone.
There's a bunch of subtle variations on this concept, mainly how the initial hover to the pillar is done as well as to what extent the megaflips are curved. In this video, the megaflips are somewhat straight, but another common strategy is to curve the first one far to the left (by holding right), make the second one straight, and then curve the final one far to the right (by holding left).
Downstairs Boss Key skips use a lot of explosives, and as such they are rarely preferred. However if explosives are no issue, it is a bit faster to do the Boss Key skip from downstairs.
Downstairs BK skips have enormous variation, though the simplest strategy is to do 19-21 hovers straight back, then 4+ sidehop hovers directly right to touch the loading zone. You must be careful to not hover too far back or else you'll miss it. If you start sidehopping before going far enough back, you'll go back in-bounds and be on the wrong side of the unloaded Boss Door's collision.
It's possible to save a good chunk of explosives with a downstairs BK skip by doing replacing many of the hovers with megaflips, however most of the time, if explosives are enough of an issue that you need to do megaflips, it's a good idea to just do Upstairs BK skip due to the added efficiency.
Due to Snowhead's vertical layout, the only commonly used BK skip method is to ascend to the top floor, then recoil flip through one of the two corners to clip out-of-bounds. From here you can just hold the stick towards the door and Link will do a little hop into the loading zone. Doing a delayed jumpslash can help you make it to the loading zone, but it's not always required.
Typically, people use a diagonal shield turn such as this to quickly get a suitable angle for the clip.
Great Bay Temple Boss Key skips typically take place in either the initial room or the third room of the dungeon. The latter is better for if you need to collect dungeon items/fairies but is trickier, whereas the former is easier and applicable in situations where the dungeon's optional contents are not important.
There's a wide variety of subtly-different methods to skip the GBT BK from the very first room of the dungeon. They typically all require doing a bomb ledge clip as Zora, then doing a recoil flip into the loading zone. Most of the subtle differences are in how to do the clip portion.
There's a variety of other, older methods on the GBT page, but this method has very simple inputs, so it should be easy to learn. The clipping method also doesn't lose any time to any of the methods with more complicated inputs, however there can be time saved on the recoil flip portion by not aiming Zora fins.
Recoil Flip Steps:
In most categories where it is required to go deeper into the temple (typically to collect stray fairies, dungeon items, or the Ice Arrow), it is faster to skip the Boss Key from inside the central room (the one which contains the impeller). Impeller is the word for a device that mixes fluid using external power; in this case from the waterwheel. (Essentially it's the opposite of a turbine).
The typical place to do this BK skip is on the barrel platform after collecting your 15th fairy from the barrel. The goal is to clip under the platform, then swim out-of-bounds over to the boss loading zone. Swimming in water that has no collision beneath it causes a void, so you must be careful to remain above the water tunnel as you swim. You won't be able to see it, but you can learn its path and form your own visual cues for when to change stick directions. The directions you should hold are listed in the descriptions of the videos linked below.
To clip, the main methods are to either roll diagonally into a wall near the left corner of a platform and press target on the first frame Zora starts falling, then hold A to fall, or by sidehopping into a ladder and continuing to hold A to fall. Both of these methods are about the same speed so it's just a matter of personal preference.
There are also a wide variety of possible BK skips in ISTT, though they can all be generally grouped into either "left side" or "right side". Neither of these actually takes place on a given side since the boss loading zone is perfectly centered left-to-right in the dungeon, so the names are based on whether you take the left or right door out of the first room.
Left side boss key skips take place in the downstairs portion of the central room of ISTT. Left side BK skips are faster in isolation since they skip more of the Temple, but they do use more explosives and they require chus to be fast.
The best setups involve hovering up through the bottom of one of the walls of the central platform (with a Deku flower and two pots). Being inside one of these walls enables you to get through the invisible collision surrounding this entire room since there's no collision on the backside of them.
The lowest explosive count setup for RTA involves jumpslashing onto the groove in the wall, doing a curved-right megaflip (by holding left), then stopping it on a particular frame and doing an angle change. From here, you can megaflip straight back into the loading zone. It should be 2-3 megaflips worth of distance depending on how good they were. In this video it was 2 megaflips and 1 distance hover.
Right side BK skips happen from the room with the boss door. To get there, enter the door on the right in the first room, remove the sun block, ride the updraft to the walkway, recoil flip onto Eyegore bridge, kill Eyegore, and then open the door.
The main advantage of Right Side BK Skips is they don't require chus (or many explosives at all really). The downside is that they are slower in isolation due to having to go through much more of the temple. But in a route without chus, this method is ideal!
Once inside, you can stand a somewhat precise spot and do a recoil flip to get a "ground clip" through the sloped ground near the boss door. For this, the height matters much more than the speed, so even a weak recoil flip will do. This is demonstrated in the below video.
A more common position setup than the bonk one shown here is to target the wall, do 2 fast vertical slashes, and 1 slow vertical slash. That will get you in a good position to shield turn and recoil flip.
Another alternate position setup is to target the wall, crouchstab twice, then vertical slash twice.