There's no point trying to lube a dirty drivetrain. At the very least wipe down everything you can (chain, cassette, derailleurs, etc) with paper towels, remove as much black grime as possible. If you have time and tools, take it completely apart and soak in a plastic bucket with degreaser (simple green or krud kutter), then make sure to lube all bearings. To take off the cassette, you need a chain whip and a cassette lockring tool, there are a few different lockring tools and you need to get the one that matches your bike. To take off cranks and front rings, you'd need custom tools too, but you may be able to get away with unscrewing and taking off some of the rings without removing the crank.

If you're worried about doing this inside the apartment (and for a good reason - bike grime is very hard to get out of the carpet), Home Depot sells plastic sheeting for something like $1 per 10x10 foot sheet. Look in the paint department.