My child has a cold, how long until they can go back to school?

Depends. If a child has a fever, they should be home 24 hours untreated with no fever before going back to school! otherwise, if they are acting normally, eating fairly well, and sleeping at night and are pretty good with using their "secret space, " the inside of the elbow for coughing or sneezing into, and hand washing then they should be ok to be at school, i doubt they were the first case anyway.
Depends on severity. A few days, at the least until the fever is gone. If the child is really sick, keep them home until the fever is gone and they are able to drink and eat reasonably well. Otherwise you will probably see that they are sent back home from school.