Here is something I do before I start sitting on the pot of a public toilet. I would pull out a few squares of tissue paper to wipe the surface of the toilet seat. This will actually accomplish two things. The first is to make sure there is tissue paper in the stall. The other which may not seem so obvious is to creat a static charge on the toilet seat. Most toilet seats are made of plastic. Rubbing it with paper will give it a charge. This will make the paper toilet shield stick to seat and not move around before you sit down.
This one is strictly for the guys. How many time have we been told that we should aim to the center of the toilet when we pee. That is actually not a good idea because we will just splatter the toilet water out from the center. The better idea is to aim off center near the back of the bowl. The water will still splatter but then the water spatterring toward the back of the toilet will be caught by the back of the bowl. And the water splatterring toward the front of the toilet (where you are standing) will have a longer distance to travel. Hopefully it will land in the bowl instead of you. There is also a second thoery if your aim is good you can aim to the left of the bowl. The force of the spray will cause the water in the bowl to spin, there by forcing all spatter to head away from you.
It is always better to not get anything wet.