I got this recipe from Cooks Illustrated, and have gotten compliments on it since then:
Allow the Meat to come to room temperature (more on the cut of meat to use later), about 4-5 hours.
Rub the outside of the roast with olive oil and then smear spices on it--I generally keep it simple with salt/pepper/toasted onion powder and garlic, maybe a little celery salt instead of regular salt.
Put it in a large dutch oven on top of the stove, and sear each side until nicely browned.
Put the meat (bone side down if it still has the bones, on a rack if it doesn't) in a pan, put some beef broth in the bottom of the pan--not enough to touch the meat itself, just to keep a moist environment, and to be filtered later for the Au jus to go with it. A splash of red wine is good in the broth also.
Put it in a 200 (Two Hundred) degree oven for about 30 minutes per pound. You need a good oven thermometer to make sure of the temp. Up to 225 is fine also. A good in the roast meat thermometer is a great help, or a good instant read thermometer--try not to open the oven very much during the cooking.
Use the standard scale--about 120 for rare, 135 for medium, 145 for med/well, and screw you if you want a nice piece of meat done well. It will be a little pinker than you are used to in a steak, but will be damn close to a good (you need a real prime rib oven for GREAT) prime rib in a restaurant. Serve after it sits ONLY 5 MINUTES!!! A regular cut of roasted meat is supposed to sit for 15-20 minutes to let the meat juices re-distribute throughout the roast, this comes out a little too cool to do that with, and doesn't need as much resting time.
The cut--a Bone-In Rib Roast (the same thing the Rib-eye steak is cut from) works good, or a boneless Rib Roast is fine also. The bones are good for soup or for a dog to gnaw on. If you use the boneless. There are 7 bones (a butcher would know how they are numbered, but I am not sure) in a standard Rib Roast. Usually you get it cut into a 3 bone roast and a 4 bone roast. I get the one with one solid piece of meat in the center of the roast. At the other end, it separates into 2 pieces with a layer of fat in between.
I have tried a Select Cut from the local Grocery store, and it turns out a little tough. Get Choice at a minimum, and if you can find Prime grade beef, DEFINITELY go with that, as it will be worth it on the table.
I serve it with the strained Au-Jus from the bottom of the pan and a creamy horseradish sauce. (Mashed 'taters and sautee'd mushrooms go well with it also).