I recommend doing volunteer editing first to get some experience under your belt. There are plenty of e-zines that use volunteer editors, and even some e-publishers who hire editors and pay them based on the sales of the e-books they edit. If you want to get into fiction, you might even want to spend some time in a critique group like SFF/OWW or Critters--not just to get experience reading fiction with a critical eye, but also to learn from what other critters are saying in their critiques.

I also highly recommend taking some courses in editing. The Editorial Freelancers Association offers excellent courses and several booklets to help new freelancers get their start in the business. Katharine O'Moore Klopf (also a member) maintains an extensive copyeditors' database on her Web site.