There are a bunch of ways to do it. Some use sand, others prefer hay or straw (there are several types of each). Lots of people use wood shavings, as they are cheap and easy to buy in stores. I know that at least some people use leaves or grass clippings from their yard, this works too and is free.
There are pros and cons to every method out there, and many can depend on the climate where you live. For example, if you live in a super windy place, you probably shouldn't use sand bedding, at least not in your run. It will get everywhere! Whereas another person in a another part of the world might love sand for it's ease of cleaning and scooping. It really depends on what you prefer I think. One person who has tons of trees in their backyard and who doesn't mind bustin' out the rake will probably use leaves, somebody next door to them who also has trees might dislike all the work that entails and instead choose wood shavings.