Disclaimer: there are many many ways to care for a bike chain, and different riding conditions may favor different lubes.
When commuting in Chicago, I used a similar method to this, but just used a quality dry lube in a spray bottle with a thin tube tip.
What ya need:
Oil: just a couple ounces. You can use regular motor oil, gear oil, or even synthetic, experiment.
Paint thinner. We call it "mineral spirits" over here.
a chain cleaning device of some sort, or a toothbrush
some rags
Updated: mix the oil and solvent 1:1 if you want a good film, 4:1 if you want a really dry chain.
In the garage or a space where you can be a bit smelly and messy, secure the bike in a position where you can easily turn the pedals backwards.
Place rags under the chain, and tuck some into the spokes so lube doesnt spash onto your rims.
If you have a chain cleaning device, fill it with the mixture and back pedal till the chain is no longer "crunchy" when flexed side to side.
If you use a toothbrush, scrub the chain with liberal amounts of the mixture on the bottom bit, letting the solvent/oil mix drip off with the dirt. Keep doing this till the chain is no longer "crunchy".
Wipe the chain dry with rags. Also wipe the chainring you used dry and the jockey pulleys on the derailleur.
Let the chain sit overnight. The thinner will evaporate, and the lube will be inside the chain where it belongs. Wipe the outside again if it feels a bit oily.
Ten minutes tops.
and cheeeep.