Public bathrooms are where the kings of germs hold court. And they, like Joffrey, couldn't care less about your health.
If you sit:
If the stall doesn't provide you with toilet seat covers, take a couple of strips of toilet paper and lay them on the toilet. Or, if you have some hand sanitizer on you, you could squirt a bunch on the seat and rub it down with TP. Sit (Unless it's SUPER gross, don't squat! You might miss and then YOU'RE the person making the bathroom germier) and get 'er done. You can flush with your foot, but you're going to wash your hands anyway RIGHT?
If you stand:
Just don't touch anything, and wash your hands. Duh.
Wash. Your. Hands. And don't touch the door handle after you've done it.