OneMakaron discovered easy setups for the angle that work for both sword and swordless DoT skip
This angle setup uses c-up, which is useful sometimes and can help you understand the trick better.
Get against the left wall near the DoT. Press Z to make sure the camera is perpendicular to the wall. Turn around quickly (straight back, not at an angle), and try not to move forward either. Whether you do or don't move forward, press Z and strafe into the corner so that when you align it in the next step, the angle and positioning is the same every time.
Line up the pointed part of your swords handle (the left and highest part of the handle) on the sword icon, with that crack between the 2 wall textures:
Then hold Z, and then leave C-UP view while still holding Z.
Now, very lightly tilt the control stick diagonally to the bottom left. If the 'A' button doesn't read JUMP then you are good (as long as it's tilted a bit). Press A and then as the roll starts, you can now move the control stick all the way diagonal as far as it goes and mash A. Link will roll into the corner and if you time the sidehop right then you will get through it almost every time.
Whether you get far enough after clipping to stay in the wall, or if you get spit back out depends on how late you wait to jumpslash after you clip through the wall. So don't jumpslash too early or you won't get through (or stay in), but if you do it too late then you will die. At least if you get spit back out, you still have the proper angle and can keep holding Z and just use a bottle to sheath your sword. Then you can do it again. This is faster than dying at least and having to set it up again (as well as the falling time, and the time it takes to run back over there from the entrance).
If you are having trouble timing the jumpslash, you may want to try pause buffering. By pausing after the sidehop you can move 1 frame at a time until you find the specific frame to jumpslash. The frame you need is when the camera is still in bounds but Link is no longer visible because he is OoB. When you find this frame, unpause, hold left and mash B and you should make it in.
Beware though, there is a false frame that looks similar to the buffer frame. If you hear Link gast the frame you pause, you are already too far and wont make it.
In certain circumstances it is necessary to skip the Door of Time without a sword. Doing so is slightly trickier than the normal Door of Time skip. Align with the left side of the door just like you would do for a normal Door of Time skip. Now backflip and press C-up. This makes sure that your angle is correct since Link's angle changes very slightly even when standing still. Now set your angle so that the left side of the R in "Return" is right where the right side of the rightmost seam of the Door of Time. This angle is more precise than the usual angle.
The next part is clipping out of bounds. This is done the same way as normal — sideroll, and then sidehop. Before you fall out of bounds, make sure you release Z and the control stick. The timing for the next part is similar to the above method. Press Z on the same frame you would jumpslash (first frame where you can't see Link). Too early or late and you'll end up falling oob. When you hear Link do a jump hold left and you should be through. If you are pause buffering, hold left on the frame where you can see Link's hair. The amount of time you have to press left and still make it through is pretty lenient.
The most notable use of this trick is using it to get a stick on B from Lon-Lon Ranch for any% runs. This skips going to the fishing hole for RBA. More info on Lon-Lon Stick on B soon to come.
There are 3 ways to skip the Door of Time as adult Link:
Giant's Knife clip (also works with Biggoron's Sword). This is not very common due to requiring the GK or BGS, but is the easiest and quickest. It also requires Hover Boots.
Recoil boost. This is the most common method, and requires the Master Sword, a shield and Hover Boots
RBA Odd Potion for the Song of Time (note: for the song to work, you need to enter the Temple of Time from outside. Simply warping in with Prelude of Light won't work). This method is useful mainly only for bingos or puzzle goals.
This method requires either the Biggoron's Sword or the Giant's Knife as well as the Hover Boots. Look at the crack where you would normally do DoT skip. Aim at it at a 45degree angle and use a triple thrust with your sword (Z Target + Forward B). You will clip on the 3rd thrust, assuming the angle is correct. As soon as you clip, side hop to the right to land back in bounds on the other side of the door.
To get out of the room as adult you need to either savewarp or use an OoB hover boost from an acute angle pillar which requires early hover boots. Jumpslash into the pillar and slightly tap a direction so you don't get pushed back in bounds. Angle yourself so that you are facing the opposite side of the room as seen in the video. Now hold Z and move slightly right or left (depending on how far you moved during the clip) until the hilt of your sword is slightly in bounds. Now let go of Z, hold R and press B to crouch stab. On the 2nd frame your sword hits the wall (sparks should be going out a bit and you should notice you have moved) pause and equip hover boots. If you didn't move when crouch stabbing then you may want to move forward a bit. If you didn't hit the wall move slightly left. When you unpause, hold backwards and roll, and about 1 second after hover boots deactivate, press B to jumpslash and you should be in the unloaded front room, free to leave.