Two main concerns when sitting: maintain decency and don't wrinkle the pleats.

Here's the drill that will soon become instinctual to you:
-as you're on your way down, do the under-butt swoop [keeping the pleats in line].
-spread your legs wide-ish, and then return them to a less splayed state [creating a natural droop in your front apron, which is often enough for decency by itself]
-while you're doing the above, you will want to gently press, or lightly 'chop' the apron in between your legs [to ensure that it drops sufficiently].

It also helps to 'scoot the boot' as Steve says in order to help maintain pleat integrity, and always ALWAYS be aware of anyone with a lower vantage point than yourself. If you're on a raised platform relative to anywhere else, or there are kids, midgets, or people sitting on the floor around, you'll want to keep extra close watch on the droop of your front apron.

In school, the only one facing you would be your teacher, and he/she would be standing or sitting at least at your height, so no extra worries for you there.

For a crouch, you'll want the same push/chop, and keep an eye on your front apron! You'll be paranoid for a while, but eventually you'll not even think about any of this.

What you really need to watch out for are weird air-pressure scenarios.
-standing near an obstacle [wall, car, etc.] on a windy day. Better to be out in the open.
-dust devils, or other unpredictable weather happenings.
-floor mounted vents [GREAT if they're air-conditioning vents on a hot summer day!]
-street gratings/sewer openings where warm air will rise
-any crosswinds [at intersections, edges of buildings, etc.]

It sounds like a lot, but it's really not something to worry about. It'll all come naturally. You'll feel the kilt start to rise and you can casually place your hands there to halt it without looking panicked most of the time. Once or twice, it might just be fated to fly up, and you must keep a good sense of humour about it, since your reaction will be a guideline for those around who may have witnessed it. If you act like it's slightly amusing, but no big deal, then so should they. If you act mortified, you will be mocked. Same with anything in life. Homo homini lupus, as they say.

Anyway, I'll bet that even with all of this rambling, I still missed something. It'll be added to soon enough.