How do you know how many light fixtures a 15-amp 120-volt circuit can hold?

Depends on the fixture rating which is sized by the bulb wattage. For example, if you were using 60 Watt incandescent bulbs, they draw about 1/2 amp each. For a worst case continuous load that would be 80% of 15 amps = 12 Amps so it would be 24 fixtures rated for 60 watts each.