Velo Dog

Sorry--I should have included that. The black stuff is probably a combination of lubricant, either grease or oil, and dirt. You can get it off (except for the chain) with any solvent (WD-40 works) and a rag, brush, Q-tip or whatever's appropriate for the space. Depending on how far you want to disassemble the bike, it can be quick or tedious to get it pretty clean, and there are a few tricks. For instance, you can run the edge of an old towel between the cogs on the cassette or freewheel and just pull it back and forth. The cassette will rotate in one direction but not the other, and pretty soon it's clean. Some people spray the whole driveline (chain, derailleurs and all the gears) with WD-40, let it stand a few minutes, then wipe it all down.
The chain is a special case, because it has so many parts and little crannies. A lubricant like ProLink (from a bike shop) works well and doesn't leave much residue.
I'm assuming you don't have many tools or much bike-specific stuff and that you don't want to take the bike apart. If that's the case, here's a chain procedure that isn't ideal, but will work: Spray the chain with something like WD-40, rotate the cranks backward several times, then leave it alone for a few minutes.
Now, take a rag or old towel (you're going to ruin it), grasp the lower part of the chain with it and rotate the crank backward while wiping the chain, moving to a fresh part of the towel as needed. You'll be amazed how much crud comes off. You'll probably have to repeat this three or four times before it even looks a LITTLE clean.
When it's shiny enough to suit you, wipe it once more, then apply a chain lube like ProLink or White Lightning (bike shop; ask for a recommendation if you're not sure) according to instructions. Repeat this a few times at, say, 200-mile intervals, then lube periodically. ProLink itself is a pretty good chain cleaner, but too expensive to use that way.
Or get a new chain, as the other post suggested, and clean and lube that.