How can a child at birthday party give all the other children chickenpox?

Children are given a vaccination so this would not happen if all are properly vaccinated. Otherwise an infected, unvaccinated or previously diseased child would need to come into contact with other unvaccinated /previously uninfected children at the party or before so as they were contagious by the date of the actual party. Then it is likely there'd only be an infection or two as chicken pox does take time to manifest (the first rash appears anywhere from 10 to 21 days from first exposure to the virus); it is contagious from about a day or two before rash appears until all have crusted over, usually another three or five days depending on the person and care of the sores.