It’s important to change your Driver’s license first, so that when you go to change everything else, you have ready proof of your new name.
Each DMV will have its own form for changing your name. Find your DMV online at www.dmv.org.
Regardless of state, you’ll need a copy of your marriage certificate, as well as appropriate forms of ID (passport or birth certificate).
Some states will require that you change your name on your title and registration of your car, as well. Each state’s site should have the appropriate information.