Ask your doctor's office to submit the prescription claim for you. If they are willing to allow you to pay your usual copay for your prescription and seek the balance from your insurance company, similar to the procedure you are used to at a pharmacy, then you shouldn't have to worry about submitting the prescription at all. Doctor's offices have different policies on submitting to your insurance for you, so discuss this option with your doctor up front.
Contact your insurance company. Ask them how you can get the paperwork to submit a prescription claim and the proper procedure for doing so. Find out what kind of supporting documentation you need for your claim, the deadlines for submitting and when you can expect to receive your money. Be sure to be clear that you're receiving your prescription via your physician and not a pharmacist. Since there is technically no prescription being written, there may be special rules you need to follow.
Submit your prescription claim. Follow the instructions to the letter to avoid any problems in receiving your reimbursement for your prescription charge. Keep a copy of your claim form and records on your submission and any interaction you have with the insurance company while the claim is being processed, in case any problems arise.