What is the proper way to store steak at home? When you buy steak from the market it is usually wrapped up under shrink wrap and the meat usually sits on top of a moisture absorbing pad. When you get it from the butcher, it is wrapped up in waxed paper and/or brown paper.

Once you get it home, if you're not going to eat it for a few days, what is the proper way to store it?

The reason I ask is that if I let it sit in the waxed paper for a few days, when I open it up, it looks slightly discolored on the surface, with a slightly slimy texture. I'm assuming that this is okay because I've cooked may steaks that looked like this and have not gotten sick.

Should I take it out of the packaging and have it just sit on a plate? Does this emulate dry-aging? Taking it out will definitely prevent meat from getting the slimy texture.
The discolored surface is a product of oxidation, the same thing that happens when you leave apple slices in the open air. Oxigen is a highly reactive molecule and it binds to anything it can find, in this case your steak.

It is not rotten or unsafe to eat in any way, it just has an unpleasant color/texture when raw. Meat packaging is often filled with carbon dioxide, and since the oxygen is already binded to carbon it no longer reacts with the steak. The side effect of this is that your steak could have gone bad, but it still looks good. The pad just collects any fluid that might  drip off the steak, again for aesthetic purposes.

I'd suggest to remove the wax paper and shrinkwrap it, this will prevent it from oxidizing.