Mine usually start to build queen cells in early/mid may. I then separate the (old) queen from the the flying bees to prevent swarming. I take a frame with one good queen cell (preferably unsealed), put it into a new brood box and also add fresh (foundation only) combs + the supers. I then put this "new" queen in the place of the hive and move the "old" broodbox (with all other queen cells removed, but hopefully the old queen in it) to a new place at least one, but preferably two metres away. This means the flying bees will return to the old place but with the new queen, and the old one doesn't swarm. The old hive (at the new place) will need a super in about a week/two weeks, as nurse bees start flying. At the end of summer I try to unite, and if I see her will kill the old queen (depends on how old she is).
It doesn't always work, especially if the queen cell had already been sealed, they might already have taken off....
However this way you don't have to find the queen (I am not very good (patient) at this), you only have to make sure that she is NOT on the frame you put into the new hive. This year all three of mine have been successful, in that all three have new laying queens in them, but two of the old ones have died (or had already died when I did the swarming procedure), so so far so good.
I found one book very good, the "Teach yourself beekeeping", it describes this method. The other bee book that I htink is fairly simple (and understandable) is "Bees at the bottom of the garden".
