There should be a number on the back of your insurance card to call and ask. Usually, insurance does cover annual exams, and docs will often test for stds at that time. You might still be charged a lab fee or processing fee or some other crap even if insurance does cover it.

If you need treatment and your insurance does not cover it, you can try to look up planned parenthood in the phone book and ask if your local one offers free or reduced services. They do testing.