I don't know what state you're in, but in my state (Texas), if you're at least 18 years of age you don't need to obtain any sort of "learner's permit" (actually, a restricted license) in order to apply for a fully unrestricted driver's license.
What you do is: Go down to the nearest DMV office, pay the application fee, and take and pass the vision test, and the written test and the road test. If you pass all 3 tests, you'll be issued a driver's license. In the larger DMV offices, all 3 tests might be completed on the same day. In the smaller offices, you'll probably have to make an appointment to take the road test. You get 3 shots at passing the written test and/or the road test before you have to pay another application fee.
Passing the written test becomes your "permit" to take the road test. You won't be allowed to take the road test until you've passed the written test.