Re-queening is the replacing of the old queen with a new one.  When the bees do this themselves, it is called supercedure.  When the beekeeper does it, it is called re-queening.

Re-queen your hives at least 2 months before the main honey flow so the new queen has enough time to lay many eggs. This way the hive will have many workers to make honey.  Or you can re-queen your hive after the main honey flow is over.  This way you do not lose any honey production.

1. Let the hive raise a new queen:  The easiest way to re-queen your hives is to just kill the old queen and let your bees raise a new one.  If your hive does not have any eggs, you must give them a frame of eggs and young larva so that they can raise a new queen. 
2. The disadvantage to this method is that it will be one month before your new queen is born, goes on her mating flight and begins to lay eggs.   No eggs will be laid in that hive for one month and no new workers will be born.  Another possible problem is that not every virgin queen comes back after her mating flight.  You could be left with a queenless hive. 
3. Buy a new queen:  A better method is to buy queens or raise them yourself ahead of time. Then you have them ready to re-queen your hives without having to wait for your bees to raise them. Capped swarm cells make excellent queens.  Find out when swarming season is in your area and be ready to harvest swarm cells.  Use these cells to re-queen the hives.  Topic 13 describes how to introduce a queen cell or caged queen.
4. Splitting and uniting:  Some beekeepers split all of their hives after the main honey flow is over.  They remove the old queens and put them in splits or nucs.  They leave the old hives to raise new queens.  When the new queens have mated and begun to lay eggs, the old queens are killed. The splits are united with the old hives.  The beekeeper now has very strong hives with young queens ready for the honey flow.