Like others, I use a wall. If I'm in a public restroom, I try to use the handicapped stall, which is uaually against the wall, rather than the cubicle wall. I have to have my pants down below my knees, and I feel like that would be a little obvious if I were leaning against the wall of a cubicle.
Anyway, I stand in front of the wall where I'll lean, take out a clean brief, fold it lengthwise as others have described, then put it around the back of my waist so it's centered and the waistband is at the right height. Then I lean on it, bend down to reach between my legs and grab the front of the brief, and pull it up between my legs. I make sure the standing leak guards and the leg gathers are seated properly in the crease between my thigh and crotch, then I hold the front against me with one hand while I peel one of the upper tapes with my other hand. I stick it in about the right spot (knowing how a specific diaper fits me helps a lot), then do the same with the other upper tape, making sure that the waistband is the proper tightness and that both sides are symmetric. Finally, I do the lower tapes so that I have the right amount of tightness around my thighs, slide my pants up (making sure to flip the zipper tab downward - I've torn diapers on the zipper tab a few times!), tuck my shirt in, and fasten my pants and belt.
I used to do the lower tapes first, but I've found that I have an easier time getting them done correctly if I start with the upper ones. When I first started needing to wear briefs, I first learned how to change them lying down, but that's not very practical in most restrooms. Now that I've learned to change them standing up, I can't even change them lying down anymore - they come out all off center and asymmetric.