Some people love ribeye; some want porterhouse; some love strip steaks. It doesn't matter which kind of steak you buy: look for good marbling (streaks of fat running through the meat); you want to look for steaks that have at least some outer fat on them, though avoid steaks that have a ring of fat all the way around, since they tend to turn to rubber bands.
You'll probably buy USDA Choice steaks, which are fine; if you want USDA Prime, you'll have to go to a speciality butcher and pay more, though the quality will be higher.
Organic steak does not taste different than conventional steak, "natural" steak doesn't mean anything, and whether you want grass-fed, grass-finished or corn-fed is a decision you will need to make, since there are strong opinions about each.
Dry-aged, however, is a good thing. It means the steak was hung and aged in a cold room without marinades or wet rubs. Dry-aged steak tastes much, much beefier, since some of the water has evaporated out. Don't be put off by the appearance, either: it looks dried-up, gross and moldy. Your butcher will trim your steaks for you (or should, anyway) and they will come out looking perfectly fine.
Ask your butcher if he or she will cut the steaks for you to order; this way you can specify the thickness. While there's something to be said about grilled diesmillo (usually called "carne asada"), there's nothing to beat an inch-and-a-half thick porterhouse or ribeye. "Two fingers" is a common order; the bigger you are, the bigger your steak.
2. Prepare your steak.
An hour before you want to cook, take your steak out of the fridge and put it on a plate on the counter. You want the chill to come off, or you'll have seared outsides and raw insides thanks to the laws of heat transfer. About 20 minutes before you're going to cook, sprinkle the steak on both sides with a liberal amount of coarse salt (kosher salt is fine, you don't need to use the fancy sea salt here).
Do not pat your steak dry! The juices that collect on top will help the grill give your steak a delicious crust.
3. Prepare your fire.
There are two schools here, both of which will yield good results. One is that you can essentially sear the meat to the correct doneness over roaring high heat. This is the steakhouse method, where steaks are broiled over 1800ºF fires. Doing it this way is fast and dramatic.
The second way is to sear the meat over high heat on one side of the grill, then to move it to a lower-heat zone and let it bake to the correct doneness. This is slower, safer and more fault-tolerant, and is the usual method taught to beginning grill cooks in public cooking classes.
The problem with the first method is that it requires constant attention, both to douse flare-ups (which are inevitable) and to make sure the steak does not overcook. Thin steaks will almost certainly overcook with the first method, which is better suited to big, manly porterhouses and ribeyes.
If you are using the high-heat method, you will want the highest heat you can possibly muster; in a gas grill, turn everything up as high as it will go. In a normal kettle-type charcoal grill, use about 30 chunks of natural charcoal.
If you are using the mixed-heat method on a gas grill, turn up one side as high as it will go and turn the other side to between low and medium. For a charcoal grill, take the same 30 pieces of charcoal, but pile 20 on one side and 10 on the other.
A note about charcoal: use natural chunk charcoal, not easy-light briquettes. The briquettes are, as advertised, easy to light but lend an unmistakable sooty flavor to your meat. You can make up for the difficulty in lighting by buying a $10 chimney starter. Put your charcoal in the top, then wad up a few pieces of paper (interior pages of old OC Weeklies work fine), sprinkle with a little cooking oil. Set the paper under the chimney starter, set the whole thing on a fireproof surface, and light the paper underneath with a match. Wait ten minutes and you'll have beautiful, ash-colored charcoal ready for deployment.
4. Cook your steak.
One dry-aged, grass-fed, local, USDA Prime ribeye, grilled medium-rare and rested. Notice there is no juice running everywhere.
Set your steak on the grill over the high heat and don't move it until it has browned nicely on the bottom. You don't need oil, you don't need butter, you don't need anything since the fat in the meat will keep it from sticking too much.
If you are using the high-heat method, you will keep the meat over the fire for a longer period and do exactly one flip. Your cue to do this will be when the brown color has moved slightly less than halfway up the outer edge of the meat. Flip the meat and cook until done (see below for doneness).
If you are using the mixed-heat method, as soon as you get char marks (about a minute and a half to two minutes a side), move the steak to the cooler side of the grill and cover. Cook until it gets to the desired doneness. There is no clock on this; you will have to watch your steak and test for doneness.
If you are a novice griller, you should use an instant-read meat thermometer. Insert it lengthwise into the center of the meat and let it register the temperature. You want to pull a rare steak (cool red center) at 125ºF, a medium-rare (warm red center) at 130ºF, and a medium (warm pink center) at 135ºF. These are not the final temperatures, but as the steak sits you can count on a 5-10ºF increase in temperature. Once you hit the target temperature, don't remove the thermometer from the meat, lest the juices run out of the hole.
As you get more familiar with your grill, you can start doing the face test. Jiggle the bottom of your earlobe. Feel how squooshy it is? That's what a rare steak feels like when you press it. Open your mouth slightly and jiggle your cheek. That's what medium-rare feels like. Jiggle the side of your nose; that's medium. As you practice, you'll be able to judge a steak's doneness with increased accuracy.
5. Rest your steak.
If you've followed all the rules up to this point, you will have a very good steak. If you follow this one, you will have a great steak. Steaks need to rest. It will be so tempting to cut right into that amazing-smelling piece of meat, but if you do that, all the juice that belongs in the steak will run right out onto the plate.
Once you have evacuated your steak from the grill, put it on something--a plate, a board, a banana leaf, it doesn't matter--cover it loosely with foil, and let it rest for at least five minutes per inch of thickness. This lets the juice re-absorb into the meat. Fear not, the steak will still be plenty hot inside.
Once your steak has rested, you can slice it if you're not serving the entire thing to one person. Always slice across the grain (that means cut across the long fibers of muscle). This makes the meat easier to chew and gives a much more tender feeling in the mouth.
Any sauces you want to add to it can be served with it at this point, but honestly, why let anything get in the way of the meat? Pair with some potatoes, a sprig of parsley, and a dry martini, a big bold Cabernet Sauvignon or a big, dark beer. Happy Father's Day!