Well, first you go to the motel's web site! (For a short stay you want to go to a motel, which is a drive there and park your car in their parking lot affair, hopefully finding a parking space in front of your room, rather than a hotel, which is more upscale and more like renting an apartment.) The web site will tell you the check-in time (say 3pm) and the check-out time (usually 11am the next day). The web site will tell you the price. You can usually reserve a room over the phone or on the web site, but most motels will require you to check in in person, be over 18, and present a picture ID. They might take a copy of your ID! A place like Motel 6 will let you get a 1 bed room for 1 night.
See, it's really rather easy. If you're going to be so nervous that you make them wonder what the hell is wrong with you, you might want to bring a friend and get a 2-bed room. Let your (less flummoxed) friend reserve the room. And just don't make too much noise.
(One time my African American wife and I were staying in a small town in Idaho and I reserved the room, because I'm white and we had a bad feeling about what might happen if they saw her. Not kidding.)