And just how is it going to help you to learn about writing letters if someone else writes the letters for you? Be kinder to yourself and make the effort on your own. You could start with
"To Whom It May Concern," if the recipients are not specified. Then you introduce the person you are recommending, like, "I am writing to recommend Mr./Ms._____ for the position of dentist at your clinic. _____has earned his/her _______degree at _________(name of school), where I had the pleasure of teaching..."
Then you mention the grades the person (you) got in that course, his attitude toward work and studies, his skill (if actual dental work was involved), his care for the feelings of the patients, and/or anything else good that the professor might have been able to observe. You can also touch upon how well you think the person gets along with his peers (and hence with his future fellow employees). You end by stating that you hope they will consider this person for the position and that you feel he/she would be an asset to their dental practice.