Best thing to do is make an appointment at your college or university career center. If you have a premed advisor, send that person an e-mail about this since every school's letter service is different.
Generally, you provide the professor with a signed waiver form that forfeits your right to view what is eventually written about you. This ensures some measure of objectivity on the recommender's part, but perhaps they'll send you a copy to read, which happens.
After the recommender has finished writing, they generally send their letter with the attached waiver form to your school's letter service. When the time comes, you request where these letters should go, and the letter service takes 10-14 business days to get them to those designated medical schools.
Again, you want to get specifics from a real advisor. Many schools have what's called a committee or composite letter, which will require a lot more leg work on your part but is an awesome service if it's available.
Good luck.
AAK