(Source)

The law states that you must use your headlights from ½ hour after sunset to ½ hour before sunrise. So, at night.

You should also use your headlights when the weather's bad enough that you have to engage your windshield wipers.

You should also also use them any time you may have trouble spotting other drivers or they may have trouble seeing you. For example, if you're on a small mountain road driving a Smartcar (so named because if you get hit while driving one, it's really going to smart).

If you need to use your high beams for any reason, make sure to dim them when within 500 feet of an oncoming vehicle or when 200 feet or less behind a vehicle traveling in your direction. Forget to turn the high beams down and the blinded driver in front of you could cause a collision. No fun.