The first thing we will see when we open the hive will be the bee's behavior.
This behavior may tell us that something is wrong with the colony even before we pick up and check any of the frames.
If the bees are:
Agitated and angry,
Massively fanning their wings with their abdomens lifted up, raised on their hind legs and
Characteristically buzzing without stopping
That is the first sign that the colony is most likely queenless.
If the bees are:
Agitated when the hive opens but quickly settle down and continue with their duties
That's a sign that the hive most likely has a queen or it started making one.
At the beginning it will be hard for you to figure out which is the strange buzzing and which is normal buzzing (especially if you haven't heard it before). But in time you will learn to notice the difference in bee's behavior.
In any case, that is just a sign that the hive is probably without a queen, but in order to be sure, you will need to check the frames.
Fanning at the entrance
At the entrance of the hive, in summer, you can see bees fanning their wings, raised on their back legs with their abdomens lifted up. This might be normal behavior of the bees which are trying to maintain the microclimate in the hive and it doesn't have to do anything with the absence of the queen.
But if you see this kind of behavior during inspection, inside the hive, that is a sign to check whether the colony is queenless.
Fanning in taken off boxes
Another thing that could happen is, while you are conducting an inspection, the bees from the taken off boxes start fanning. This happens because they are separated from the box with the queen and they can't sense her anymore.
To avoid them getting too agitated, the inspections should be done in the shortest period of time. However, you must not be in a hurry because you are likely to do more damage than good.