Sheik is infamous for her completely intangible ledgestall with her up special, which allows her to avoid on-stage interaction for an indefinite amount of time, unless the opponent succeeds with a—quite risky—edgehog attempt.
Her up-B ledgestall, usually referred to as “Shino stall”, is very easy to execute. It can be done in a number of ways that will each fulfill different purposes, and it always has a lot of input leniency due to the move’s innate intangibility.
(Note: all gfycats in this post are half speed, so that they don’t distract as much. Click on the + once to increase speed to real-time. I put a lot of knowledge into their frames, so pausing and watching them frame-by-frame might be a good idea too.
Edit: Also, the embedded gfycats are way too small, so I added external links within the text for all of them. They are a bit hard to tell apart from normal text here, so I underlined them. Most details are only visible when watching the gfycat in a separate tab.)

Fastest / perfect execution for up-B stall:

Sloppiest execution for up-B stall that still stays intangible throughout:

However, once Sheik wants to get back in the action and move from the ledge to the stage without being at a disadvantage, it’s a bit more complicated.
Compared to most other characters, Sheik can retain a great amount of ledge intangibility into grounded actionability (this will be shortened to galint from now on—grounded actionable ledge intangibility): Eight frames with her up-aerial interrupt, and up to 13 frames with her ledgedash (upper and lower gfycat, respectively):

The goal of this post is to explain how to get as close to these magical 13 frames as possible. This time, I will not go into the underlying mechanics, but simply show what your best options are and how to execute them consistently.

The all-around best method that works on all stages equally well is:
1. First grabbing the ledge from a low up-B stall (“no-poof stall”)
2. Dropping without fast-falling
3. Jumping immediately after dropping
4. Holding towards the stage from at least the second frame of your jump on (about 40% will be sufficient, holding forward all the way is not necessary)
5. Wavelanding onto the stage with an angle that’s between 45° and 60° away from straight down.

Doing so grants you 11 galint, and even if you mistime your airdodge and do it one frame too late, you’ll still have 9 galint.

Here are the two most extreme cases that fulfill these criteria to show the leniency of the no-poof stall input range that still gives 11 galint. Left is earliest possible, right is latest possible.

To briefly expand on the steps:

  1. Grabbing the ledge from a low up-B stall is necessary to equalize your ECB. Below is a comparison of Sheik’s ECB extensions, depending on which action she grabbed the ledge out of (best: left, worst: right):

    Sheik’s ECB extensions depending on what action / frame she grabbed the ledge from

    To do the no-poof stall properly, you need to drop & fastfall immediately from the ledge and hit a 2-frame window for the up-B input, so that you grab the ledge from frame 19 or 20 of your up-B. You can see the timings in the gfycat above, here’s a link to the first of the two frames. These two frames are almost the very latest ones that still allow for grabbing the ledge before the “poof”, in fact there’s exactly one frame afterwards which will give you a worse ECB extension that’s incompatible with this 11 galint input method. In the picture above, it’s the third entry.

  2. Dropping without fast-falling: If you fast-fall by accident, you will start your jump from lower and by the frame you could normally waveland on the stage, you will still be too low and airdodge against the stage wall to your death.
    So ensuring that you don’t fast-fall is important. Here are input maps for dropping with control stick and C-stick, stick positions are what I recommend:

    Ledge options with control stick (left) and C-stick (right)

  3. Jumping as soon as possible can either be done with the control stick or X/Y. If you dropped with the control stick, moving it all the way up will often take more than one frame, so in this case I recommend that you jump with one of the bottons.
    If you dropped with the C-stick, reaching a jump button quickly is only easy with either claw grip or thenar grip. If you don’t use either of these, jumping with the control stick will probably be more consistently fast.
  4. To get above the stage quickly enough, you need to start holding forward at either the first frame of your jump or the second one (with some exceptions¹).
  5. For the waveland, too steep angles will make you miss the stage, while too shallow angles will keep you airborne for an additional frame. Below are the steepest and shallowest angles that work (only for left ledge, right ledge would be mirrored):

    Sheik consistent 11 galint ledgedash angles

I mentioned before that Sheik can get up to 13 galint, so you might be confused why I only mentioned the 11 galint execution.
The reason is that both 12 galint and 13 galint are really hard to do. The latter even only works on Battlefield, no other legal stage.

To get 12 galint the same way on all legal stages, you need to regrab the ledge from a low, vertically sweetspotted rejump.
That’s only the first step, though—after that, you need to drop and jump as soon as possible and hold forward from the very first frame of your jump on. You don’t need to hold full forward from the first frame on, but you do need to hold at least halfway (about as much as I used on the left side of the 11 galint gfycat). Only the waveland angle has some leniency to it (about 40-60° from straight down).
Because holding forward instantly after dropping from the ledge is hard and the necessary rejump ledgestall before that isn’t safe, I don’t recommend using this method. But if you are set on it, you should at least take the habit of dropping with the down-forward angle I’ve shown before.

Anywhere, here is the 12 galint gfycat with inputs and intangibility:

13 galint can only be achieved on Battlefield. For this, you need to grab the ledge the same way as for the 11 galint (no-poof stall timed within a 2-frame window).
After this, also drop and jump perfectly and also hold forward from the very first frame of your jump on. Finally, for the waveland, only angles between 17.1° and 24° will make you ledgedash successfully. Lower angles will make you airdodge against the wall and fall to your death.

On the positive side, if you do manage to do it perfectly, in addition to the long intangibility you also get a very long ledgedash sliding length.

Stage-specific things

All of the below is very specific information that I gathered because Mew2king bothered me for more. If you aren’t a very serious competitive player, you should probably skip it for now or it’ll just confuse you.

¹Battlefield, due to its receding wall, also has some other oddities compared to the other stages. If you grab ledge from frames 19-20 of your up-B, you don’t need to hold forward during the jump at all to still be able to waveland after JumpAerialF frame 6 (fastest possible). This is also true on Dream Land 64. So you can drop with straight down, press X, Y or up to jump, and only start holding down and forward on the very frame you input your waveland.
Additionally, on Battlefield only, you can also still get a JAF 6 waveland even if you grab the ledge from frames 18 or 21 of your up-B. For these, you do need to hold forward like for the others (no later than from the second frame of your jump on). For all other stages, you can only get a JAF 6 waveland even if you grab ledge from 18 or 21 if you hold forward from the first frame of your jump on. On PS, FoD, YS and FD, you need to hold full forward from frame 1 on. On DL64, it’s sufficient if you hold only the slight down-forward angle that I showed works for dropping from ledge too earlier. (Even on DL64, you still need to do a 315° angle for the waveland, though. The slight down-forward angle for the airdodge would make you collide with the wall and fall to your death.)

For those who want the precise data for all six legal stages, here is a picture of the spreadsheet I made for gathering the data I used as foundation for this post:

Sheik ledgedash data