I was taught a slightly different procedure, which is the same as the one listed as the first result on Google for "jumper cables":

1. Line up the cars, pop the hood on both cars, get out the jumper cables, make sure both cars have their engines turned off, check that the dead battery looks safe (no cracks, leaks, or swelling), and try to scrape off any corrosion on the terminals.
2. Connect one red clip to the positive (+) terminal of the dead battery.
3. Connect the other red clip to the positive (+) terminal of the good battery.
4. Connect one black clip to the negative (-) terminal of the good battery.
5. Connect the other black clip to the exposed metal of the engine or chassis of the car with the dead battery. The chassis is connected to the negative terminal ("grounded"), so this will complete the circuit while minimizing sparks near the battery itself. A malfunctioning battery might be venting fumes of flammable/explosive hydrogen gas, so don't risk sparks near the battery.
6. Start the "donor" car. Let it run for a minute or two.
7. Start the "acceptor" car. It should crank and run normally.
8. Disconnect the cables in the reverse order (undo steps 5, 4, 3, 2). If the order is reversed exactly, then the cables can be disconnected from the two running cars with no sparking near the battery. You'll get some sparks when you disconnect from the chassis, but that's OK.
9. Wait a few minutes (3 to 5). The acceptor car should continue to run. If it dies a few minutes after disconnecting the cables, then it's a problem with the alternator and not just the battery.
10. Put the cables away, close the hoods, and thank the owner of the donor car (who can now leave).
11. Leave the acceptor running for a while. You can drive it as much as you like during this period; just don't shut off the engine until the alternator has had time to recharge the battery (say, 10 to 15 additional minutes).

The site I linked to makes the point that steps 6-7-8 in my procedure can damage the acceptor's alternator. It recommends letting the donor run for a bit longer than my step 6 requires, then (8a) shutting off the donor, (8b) disconnecting the cables entirely, and only then (7) starting the acceptor. Whether or not this method works would depend on the state of the battery (it may fail for a poor but working battery) and the weather (it may fail below, say, 10°F / -12°C).

(Note: lead-acid batteries are damaged by letting them discharge fully, because the cathodes and anodes are both transformed into the same material, lead sulfate. Once that happens, it becomes far more difficult to recharge the battery and you're better off just buying a new one. Even if your battery won't take a charge, a jump start can get you to a store that sells new automotive batteries -- the battery is only needed to turn the engine through the first few cycles, and the alternator will provide all needed electricity once the engine is turning fast enough.)