I do many of the same things that Sompuperoo does. I'll just put my procedure here since I handle the lifting of toilet seats and flushing of toilets differently than he does.
Open the door to the bathroom. If you are concerned about having touched the door handle, then wash your hands upon entering the bathroom.
If you wish to flush the toilet before using it, use your shoe to push the toilet's flush handle. The bottom of your shoe will already be dirty, so using it to touch the toilet's flush handle isn't a big deal, and it's a lot better than using your hand. If you wish to flush a urinal, then use the back of your hand to push the handle instead of using your fingers.
If the toilet seat is up and you want it down, or vice versa, then use the side of your shoe to lower or lift the seat. If you plan on sitting on the toilet, place a disposable toilet seat cover on top of the toilet seat. If disposable toilet seat covers are not available, then rip off a few strips of toilet paper and place them so that they fully cover the seat.
When you are done with your business, use your shoe to flush the toilet. If you are at a urinal, use the back of your hand to flush it.
Wash your hands with soap, and then dry them off with a paper towel. If there is an air dryer instead of paper towels, you may use that.
If paper towels are available, then grab one right before you leave the bathroom. Use the paper towel to grab the door handle, so that you hand doesn't touch it. Then use your foot to prop the door open, and then toss the paper towel into the bathroom's trash can. Then use your foot to push the door wide open so you can walk out without touching the door with your hands.