You'll need some liquid latex (get it at just about any costume store, ask the clerk and they'll know what you're talking about), a makeup sponge, a mirror, concealer/foundation in your skin tone, and a needle/thread (optional, for doing stitches)
Dip the sponge in the latex and pick up a little.
Dab the latex onto the mirror to make a really thin layer. You want it to be as even as possible
Wait for the latex to dry. Or blow-dry it on low if you're impatient.
Continue dabbing on thin layers and drying until the latex is the thickness you want. If you're making a scar, you can do thicker, less even layers to make it look ragged, or build up very gradually for one that looks more healed over and old. If you're going to make stitches (or just some peely skin), you don't need it to be as thick, so just add layers until it's not transparent anymore.
Peel off the latex. Try not to let the edges roll up on themselves. If they do, you can trim them off with a pair of sharp scissors or a razor blade.
Apply a little bit of liquid latex directly to your skin and stick on the "skin". Let it dry for a moment.
If you want the skin to be really smooth, stick it with the side that was on the mirror up. If you want it to be rougher, stick it the other way. I chose the rough way.
Add more latex to blend the edge of the fake skin into your real skin. Then apply your concealer/foundation. In the picture I only blended the top left edge.
CAREFULLY stick the needle through the "skin". Don't sew through your arm. It hurts.