No, your vet doesn't do it. It is a cheek swab kit that you will need to do. It comes with an instruction sheet about what to do.
First you register your dog with the Canine Phenome Project:
You will order the DNA kit from within the registration - there is a link to click on the upper right hand side of the page (New FTA based Fanconi test) and it will bring up a page from the OFA (offa.org) where you will place your order. The kit is $65. Be sure to print a copy of the confirmation as that has a login code that you can check for the receipt of the swab by the OFA and the results (before they are mailed).
I recently ordered a kit for my new puppy boy and it arrived 3 days after I ordered it. The results come fast these days - I know someone that found out their results 3 days after the swab was received back at the OFA.
You can order a test from the OFA website, https://secure.offa.org/cart.html
Also, please take the time to register your dog with the Canine Phenome Project, http://www.caninephenome.org, and fill out the surveys. It is free and helps give the health committee a view of what is going on with the breed.