Where do I start looking first? The headlights on my friend's 91 Accord, don't come on at all.

Got to do some elimination work. Is the problem just headlights or all lights, front and back? If just headlights, all power goes through the lighting relay. The relay is controlled by the lighting switch on the steering. Could be both fuses in the under hood relay box or the lighting relay or the steering switch. As soon as you figure exactly what the problem is then start replacing parts starting with the easiest/cheapest first.