No minimum age. most fields require the child to be 10-11 for insurance purposes, but there is not law.
Have someone there that knows what they're doing. High pressured canisters and paintballs firing faster than 300fps will cause harm.
the most important thing- WEAR A FULL MASK/GOGGLES MADE FOR PAINTBALL. you can pick them up at walmart for cheap. There is a good chance someone will loose and eye, have a nasty scar on there face, or something else fun happen.