Right off the bat I need to point out that this is not real dry aging. To do that properly you need a room that is at 50% humidity and is held just above freezing. Beef halves or primals are aged for weeks in such an environment, which promotes the growth of beneficial fungi, removes moisture from the meat, and intensifies the flavor. Then later on, the primals are trimmed and individual steaks are cut off and you buy them for $50-100 each at premium steakhouses.
There are ways to fake this at home with a single steak, though it works better with one steak that's big enough to feed two or three. You'll want to use a thick cut of meat, like a custom cut ribeye or sirloin. Or you can do what I did and pick up a clearance 1.5 lb. Porterhouse that's already beginning to brown a little. As soon as you get it home, dry it off with paper towels, place it on a rack over a plate or tray, and salt and pepper both sides. Chuck it in the fridge, uncovered, for an overnight rest. After only 18 hours you can already see that it is taking on the appearance of a dry-aged steak.
NOTE: If you have anything funky in your fridge, the steak will pick up those flavors. Likewise, your eggs, butter, and even ice cubes might take on a somewhat beefy aroma.
Before cooking, you'll want to put the rack/tray/steak combo in the freezer for about an hour. This is a tip from Cooks Illustrated, who suggest the technique for Argentine-style steak. This wicks away additional moisture, and keeping the center cold will help you produce a browned crust and a rare interior (i.e. maximum flavor).
Then let it warm up for another hour, heat up the oven to its lowest setting, and get a big skillet nice and hot. I used canola oil, but peanut oil or anything with a high smoke point will work. Once the skillet is hot, add a bit of oil, spread it around the pan, and toss in the steak. After a few minutes, remove the steak to the rack/tray and let the pan come back to temperature. Then sear the other side. You should get a rich brown crust, and you should start getting hungry. Slide the rack on top of the skillet, insert a probe thermometer, and then roast the steak as shown in the oven until it reaches an internal temperature of 50°C/125°F. When done, remove and allow to rest for ten minutes.
The joy of the Porterhouse is that you can carve off sections of filet or strip, and there are parts that are rare to medium depending on where you slice. Thus it's great for feeding a couple of people that have differing preferences. Here I've sliced off some portions of the strip--tender, buttery, unbelievably beefy, and oh so delicious. The previous photo shows the crust during resting, but this closeup of some slices shows how there's an even rare (not raw) consistency throughout the meat.
Is this method for everyone? Certainly not. There's a big difference between aged and rotten. You need the olfactory experience to tell the difference. Dry-aging beef or venison or even curing pork produces a range of savory, meaty aromas that can be off putting if you're used to the freshly butchered wet stuff. But there is a difference, and once you've come to enjoy it, it's hard to go back.
ADDENDUM: Paul ran a test for me with a ribeye and a digital scale. After patting it dry, the steak massed 215g. After 30 minutes in the freezer, it was 214g--practically no difference, except that he claimed a texture change from his normal method. I think the refrigerator helps, and Alton Brown has shown proof of that method in actual recorded moisture loss in his ribeye roast episode. I'll let America's Test Kitchen or Mythbusters hash this out in the future, but for now it's a fun new way for me to fix a steak, and I've been happy with the results. In a month I'll go back to the best method: spearing on a pitchfork and dipping in boiling oil.