I use my foot. I also wait to flush until I have the stall door open so I can flush and then back up quick in case there is any spray. Ick. But I don't usually cover toilet seats or squat unless they are nasty looking. Then I usually try to go to other stall that is cleaner. I do wash my hands afterwards (because I do touch the stall door nob) and don't turn the water off with a paper towel, but might start now that it was mentioned. I always use a paper towel to open the bathroom door as I leave. I open the door and hold it open with my foot and then try my best to toss the paper towel into the nearest trash. Sometimes they are too far away though. Oh well, I tried.
I also never take my purse into the bathroom because I worry about were to put it if there is not hanger. I am NOT putting it on the floor. I have to figure out some crazy way to hold it or hang it around my neck while I am going.
Edit to add: Choctaw Casino in Oklahoma has those toilet seats with the plastic that covers them that goes around on the seat on its own as well. Too neat. Love the idea. Too bad they are probably rather expensive.