Not all stations offer them but when you see the opportunity, jump on it. Sometimes students earn credit hours, most of the time people do it for the experience (that being payment enough).
Check with the local Radio stations where you live. Call or write the Program Director or General Manager inquiring about Internship possibilities.
You can see a sample letter to use as a guideline here.
Here are just a few Internship opportunities that are ongoing:
WHYY-FM, the most-listened to public radio station in the Delaware Valley, offers 20 internships in the spring, summer, and fall. Visit this link at whyy.org.
Interships at Red River Radio stations in Louisiana, Texas and Arkansas