A couple notes:

If you poke a hole in the liner installing the bottom strip that's a bit too low, all is not lost. You can pull up on the liner a bit and install the whole strip that way. Thus moving the hole either to an actual spot where there's a screw or behind the strip and sandwiched in the gasket area. If the strip is clamped tight enough the additional pressure when the pool fills the rest of the way, will only uniformly pull on the vinyl. Now if it's 3 inches below the strip your sort of sunk. But 1/2 inch or less, you should still be able to salvage the liner. You can pull up in only that section, but this sometime creates a slanted wrinkle under the stairs.

If the stairs are within 1 foot of a corner, you've got a whole set of different circumstances on your hands. Now you've got the same dynamic happening vertically on one side. Namely water pressure seating in a corner properly. On top of that, the "seating" isn't uniform like on the floor, since the water going up the side wall isn't the same in a the corner of a wall. You may need some one (or possible two) to push the vinyl into that corner while install the strip adjacent to it. There might even appear to be "extra" vinyl after doing this, or even a "crease" or "loose" area of vinyl. As the pool fills and recreates the stretching (permanently) that you performed, the extra liner or wrinkle will be stretched tight.

If you cut that "U" shaped section out of the vinyl while installing, sometimes the release in pressure can cause the top tile pattern to "sag" as it reaches the stairs. As your installing the vertical strips, do it from the bottom screws up. As you get to the screws that are just below and in the tile pattern pull up on the 1 foot of extra vinyl "inside" the stairs as you install these screws. This will remove that slight "sag" in the tile pattern. Step back and take a look at it as a person pulls up on to gauge it, it's hard to tell if it's straight when your up close.

If it rains, while the stairs are sealed off and the vacuums are running, you'll probably lose the seal, and need to turn the water off and re-tape the stairs. If there's any chance of rain keep a close eye on the stairs.


Conclusion:

These are all very basic "instructions". Each stair, it's gaskets, strips (plates if you may) the screws, can all have their own individual problems or techniques for replacing them. Until you run into them all (and you never do), there's a lot that's unknown. Prep for everything. Extra screws, extra gasket material etc. Every pool , it's wall height, location of stairs, can make a difference too. Be patient, and go carefully. If there's too much water in the pool, drain it down. Don't struggle or "force" he vinyl to do what it can't.

The dimensions of the liner can make all the difference in the world. One too big seems easier to work with, but can be hard to make the wall sections tight and not have wrinkles. A liner made too small, and it's near impossible to seal the stairs off with duct tape.

I'm not going to mince words, this is one the hardest things to do properly in a vinyl replacement. Its not only that but it has the largest potential of going terribly wrong too. The void and it's seal your creating if not done properly, cannot be patched.