If the skin is downy, there's no question: it's a peach.

If the skin is completely smooth with no down, and it's a good size, like a peach, it's a nectarine. The flesh is firmer.

If the skin is completely smooth, but the fruit is smaller and slightly tart, it's a clingstone nectarine. And of course, you can't miss the fact that the pit adheres to the flesh.