The most important thing you can do is buy quality beef. You can throw a USDA Select steak on a 700 degree charcoal grill, cook it perfectly, and it'll still be tough and not at all what you'd get at a fine steakhouse.
In the USA there are three grades of beef available to a consumer: Select, Choice, and Prime. There are lesser grades but they go to fast food joints, prisons, military personnel, and miscellaneous other weird uses.
In most american supermarkets you will find only select, period. This is an "average" steak. It's typically devoid of marbling, and results in a rather flavorless tough steak.
To find choice steaks you have to go to a higher end supermarket, e.g. Whole Foods You will pay significantly more for a choice steak, but the difference is marked. The marbling will result in a tenderer steak due to the internal fat melting and tenderizing the steak.
Finally, prime cuts. These are very hard to come by in any supermarket unless you live in a bigger city. You typically have to go to a specialty shop or butcher for these. Less than 2% of all beef is classified as prime. On top of this, restaurants get first pick. So even if you do buy a great prime steak, you are likely getting the lower end of the prime spectrum. However, the difference is amazing. The marbling is more intense, more evenly distributed and when cooked properly results in a steak that melts under your knife.
Another one-up a fine steakhouse has on you is they age their beef. Any steak you buy in the grocery store is minimally wet aged. The finest steakhouses dry age their beef. The difference? Wet aging consists of simply vacuum packing the meat (as in a whole side of cow) and refrigerating it for about a week. After that, it's cut smaller and sold to stores. Dry aging is a more complicated and expensive process. Dry aged beef is hung for at least two weeks in a refrigerator. Moisture in the meat is allowed to escape and evaporate, which concentrates the beef flavor of the beef. The beef also grows a moldy rind which is cut off and thrown away. After the aging is complete you're left with 75-80% of the meat you started with. This commands a premium price.
Unfortunately, you can't dry age a steak in your home. There are some refrigerator aging processes that you'll find on this site and others, but they aren't a true comparison.
Another variation that has become more popular is grass-fed beef. This has become a recent fad, at least in the USA. Cattle are traditionally fed corn which makes them fatter and "juicier", but it also leaves the meat tasting very bland. Likely, if you live in the USA, every steak you've ever had was corn-fed. Grass-fed beef on the other hand is fed predominantly grass, they're allowed to graze as cows should. This is good for the cows, because they don't actually eat corn. A cow is made to eat grass. Corn is rather harsh on their digestive system, but they are given no other choice. In the wild a cow would never eat corn. The end result is a very different flavored steak. Grass-fed beef has a much richer, meatier flavor. However, it's also tougher than corn-fed beef. For this reason a steak you will be served in a fine steakhouse is likely not to be grass-fed unless it is specifically designated as such.
With all that out of the way I suggest doing what I do. When I feel like an amazing home cooked steak, I'll splurge on a nice choice ribeye, dip it in a mixture of melted clarified butter and oil, season liberally with salt and pepper, and pan fry it.