Queen rearing? I have never bought in a queen.
It is not really queen rearing until you raise whole batches, I would suggest. Queen replacement for a two hive owner is a bit of a lottery. Bought in queens can give rise to horror queens after the first one or two generations, when mating with the local mongrels causes a mix of genes - not necessarily the fault of the local population, I might add.
Replacing aged queens should begin with splits at suitable times after preferably inducing supercedure queen cells as proposed above, or at artificial swarming if the beekeeper is unable to keep control of the swarming urge. Just simple beekeeping, nothing special to call 'queen rearing' really; no need to try to elevate a normal part of beekeeping to a special status! If you don't facilitate replacement of old queens, the bees will, by supercedure. You have little choice of checking the laying pattern, temperament or even getting her mated if this takes place late in the season.
Of course, it might depend on where you keep your bees, too. I don't particularly recommend rearing your own queens unless you have an apiary well away from neighbours - especially for non-thinking beeks!
RAB