To expand on what Adrian Welsh mentioned, there are many organizations that seek help with GIS work and are looking for help, even from folks with little background. There's tons of "simpler" GIS tasks that need to be done, like digitizing, that organizations need and are willing to bring in someone and train.
Many of these are government and non-profit organizations. And in terms of timing, now is a good time to look for these types of jobs, as many organizations staff up for the summer. For example, many government organizations have internships available in the summer that open up for application now (and some are only open to students currently attending college). And it is not just government - private firms that deal with field studies often need extra help in the summer months to help in study setup and then work with the data as it rolls in from the field crews.
Some specific resources:
If you are a member of the Society of Conservation GIS, they have a job board that often has internships.
Society for Conservation GIS
Also, of course, if you want to go all-out, there is this:
Student Opps Common Questions - ESRI Internships (paid!)
Chris Donohue, GISP
