Most zoos hire seasonal exhibit interpreters that allows up-and-comming keepers to get some experience. There are internships and volunteer positions available at many zoos as well. Some entry-level positions may not require previous experience, though it is usually preferred. Rarely will zoos hire full-time keepers that don't have a B.S. in some biological science though, without extensive experience anyway. I worked seasonally as a keeper/interpreter for a couple years before I graduated. There were people doing the same job as me that had four year degrees, moved from out-of-state, and made beans just to get the experience. It is not an easy field of work to break into, but it is well worth it once you get your foot in thte door. I've been working in the field for almost 5 years now, and wouldn't change careers for anything.

I hope this helps, good luck!!

-Evan