Public Toilet

Bring disposable latex gloves. Put them on before you enter the bathroom and take them off after you leave. This saves the need to wash your hands, touching dirty faucets, soap and towel dispensers.
Put disposable plastic booties on your shoes before entering the bathroom and remove them after you leave. Who knows what you'll be stepping in.
Bring your own toilet paper. There's no telling who's been touching the paper in the stall or what they've left behind.
At home, practice squatting when going to the bathroom, hovering over the bowl without actually sitting down. This is a great way to avoid the need to sit on the toilet seat.
There's a huge danger of infection if the water splashes onto you when your defecation drops into the water. Therefore, using a piece of tissue to catch your shit and drop it into the toilet after you stand up.
Needless to say, if you choose to flush the toilet, don't do it with your bare hand. Best not to flush the toilet at all, if you must, use a tissue or your feet.