The hairy woodpecker is quite a bit larger than the downy, but that's not always easy to judge when a bird is umpteen feet away from you in the woods. How the bill appears in relation to the bird's head is usually something that you can see.
The difference in the birds' bills also tells you a lot about where you'll commonly find them. The little downy is usually plying the branches of trees. The larger hairy is usually hanging out on the trunks of trees, as in my photo of the hairy.