and find the queen. There is a risk that the swarm will take off out of the box. So far, I have caught about 20 swarms and never had any problems with that, so I assume the queen is in the middle of the cluster and if I get everything, I am good. If you have an "old" queen, she is already mated and will start laying within a couple of days. You inspect it and typically can quickly find those within a week or so.
If it is a virgin queen (sometimes multple queens are spit off of a single hive) then it takes a week or two for the queen to get mated (she flies up into the sky and mates with 10 or so drones (who die in the act) to get laying eggs.
Queens lay 500-1,000 eggs a day during peak season.