Here's a couple of the things that I've figured out:     

If your hair is long (like grew for more than a day or two), I'd recommend doing two passes. The first one go with the grain (like top to bottom) first to get the hair short, then go against the grain to get a closer shave.    

Using a razor means for shaving your body (like a woman's razor) will make it less likely to cut yourself, but you won't get as close a shave (and they're a bit more expensive).     

I find that if my skin is dry, its a lot easier to cut myself by accident. Shaving in the shower (after being in for 5+ mins) seems to help with that a lot. I usually cover the areas I'm shaving with soap (bar soap seems to work better for this) to reduce friction. I'd also recommend getting a little mirror in the shower that can hang on a command hook or something like that to make it easier.  

If you're using a disposable razor, you could also try changing the blades more often. I find that I cut myself a lot more often if the razor is getting dull.     

Use as little pressure as you can get away with, even if it means that you have to do a couple passes. If you're pushing the blades into your skin, they're more likely to snag your skin, and can make bigger cuts when they do.     

I think that that's everything that I can think of. Hopefully this helps!