The hive population is growing quickly; for existing hives from last year, they may already be at 80% of their strength, and new hives will be building comb as fast as they can.
For new hives, keep feeding the bees (either honey or sugar syrup) as they need all the feed they can get to draw out the comb. Without the feed, your hive won't be able to produce any surplus honey keep feeding them till they stop taking it or until you put the first honey super on.
For existing hives from last year, it is critical that you monitor and add supers as needed otherwise your hive will swarm. When inspecting, look for swarm cells on the bottom of frames. Remove them if you can but your best bet is to monitor and add supers before they feel congested. Also, check your ventilation; inadequate ventilation (too hot) can cause them to swarm.
Monitor your hives to prevent swarming on existing hives. For new hives check every other week or so to ensure that the queen is laying and the bees are drawing out the foundation completely. If you have been feeding, be sure to keep feeding until you place a honey super on the hive or when it appears the bees are no longer taking the feed. For existing hives, you may be able to put a honey super on now or by mid-month. Even new packages should have the second brood box on by the end of the month.
If you haven't already, consider treatment options for both Varrora and tracheal mites BEFORE putting honey supers on the hive, you cannot have medications in the hive when the bees are collecting honey for human consumption. New hives probably don’t need to be treated until the fall so don't worry until after the first harvest about treating. All beekeepers need to research and pursue treatment options before a problem arises.