Aging your ribeye in the refrig is very easy
I have done this a few times. Take a cookie sheet and place some butcher paper on the bottom. Then place the cooling rack insert (if you don't have this, use a roasting pan and put the cooking rack inside it) on top. Take your ribeye roast and place it on the cooling rack and place in the refrigerator. The idea is that you want the air to get all around the meat. If you don't provide the air gap, then you have to flip the meat every day or so to keep the meat that is not exposed to the air from spoiling. How long you want to age it depends on you. I've aged for up to 30 days in the refrig. Doing it for two weeks will provide good aging. If you are trying to age for Christmas dinner, then you are starting a bit too late.
Now some things: 1) the roast will lose weight (due to moisture loss) and when you trim the hard outside of the roast. When I aged for 30 days, I lost 30% weight. So my 15 pound boneless ribeye roast came out at around 10.5 pounds after water loss and trimming. It was beautiful though!!! 2) Depending on the humidity of your refrig and the time you leave it in there, you might or might not get spore growth on your roast. Do not worry about it. When you are ready, just trim it away. I have low humidity in my frig and did not get any spore growth (I think it's fungi, but not sure). 3) This my personal note: don't age "Prime" beef. You are paying top dollar for an excellent, well marbeled piece of meat and when you age it, you are losing meat due to water loss and trimming. To me, aging Prime beef did not increase the flavor that much to offset the price of water loss and trimming. I would only age "Select" and "Choice".....but again, that's me.
Meat temps for Medium-Rare (130-135 degrees), Medium (135-145 degrees)