The Cat is right about the aging process is not for everybody.
Aging, as already established, requires controlling humidity and temperatures but most importantly the size of the piece of meat is a factor. Half cows are aged, not individual cuts, making this practice a little complicated for the home chef.
Nonetheless, I often <age> roast beef in my fridge. Although it results in a slightly more tender and definitely more flavourful meat the results are not the same as prime aging for restaurants.
Supermarket/butcher meat is already aged around 2 to 2 1/2 weeks (in Canada at least). Buy the largest prime rib roast you can afford (4 to 6 ribs). It must be freshly cut off the carcass or from the butcher counter (not wrapped in plastic). The meat should not be dripping wet like the ones in plastic wrap. Place the roast upright on a wire rack (meat up, rib below) so that air can circulate all around it. Leave in the fridge 4 to 7 days without it touching anything (no wrapping). You will notice that the surface and corners will dry up almost jerk like. Trim these dry spots before cooking.
For cooking: pan sear, without oil, the surfaces of the roast to caramelize. Smother your favorite rub (I use dijon mustard + HP sauce + salt + pepper), place the roast upright on a cast iron skillet in a 275F oven. Check with thermometer to your preferred internal temperature.
This aging process concentrates the flavour of the meat by drying it. Some natural muscle decomposition is also at work to tenderize the meat.
DO NOT use the meat if it has any puncture marks before aging and do not puncture it yourself. DO NOT use if it smells funny, becomes slimy or has any visible microbiological growth before and after aging.
The probability that a microbe will grow on the meat is reduced considerably by not wrapping the meat hence not creating a humid environment. Being exposed to cold dry air also decreases the chance of dangerous microbial contamination.