Let me throw in some tips I've found over my many years as a bike nut:
That chain tool Klein suggested, get it! I've used dozens over the years, the ones on mini tools are a pain to use and there is little leverage. The Park one is small enough to carry with you in your Camelback or in your saddle bag and is big enough to give you plenty of leverage when breaking a chain (link).
Buy one of these:
Power Link this is what everyone is talking about. You can take apart your chain in a matter of seconds. I've been using these on all my bikes for years without it ever coming apart unintentionally.
Get one of these too:
Cog Brush
I've used the "on the bike" chain cleaners and they work o.k., they seem to make more of a mess than clean the chain.
What I do: I remove the chain, drop it in a 2 litre bottle with about 3" full of degreaser (I use a citrus degreaser, but any will work), put the cap back on the bottle and shake like crazy. Let it sit while I clean my cogs and chainrings with the Park brush and degreaser, rinse with water. I then go back and shake the chain again like crazy. I fish the chain out, rinse it with clean water and let it hang to dry overnight, or blast it with my compressed air nozzle if I'm in a hurry. When dry, I reinstall it and apply a drop of lube to each roller. Yup, takes a few minutes, but I just start at the power link, and backpedal the chain as I'm dabbing each roller with a drop or two making sure it gets good penetration. I then backpedal for a minute or two to get the lube to fully coat the rollers. I then put a rag in my hand, grab the chain in front of the derailleur and backpedal to wipe off any excess.
As far as lubes. I like White Lightning (But NOT their Race Day), I like Finish Line's Krytech, and I'm currently using Pedro's Syn lube. Of the three, I'm liking the Pedro's the best! Here's a link:
Syn Lube
L8R