The following describes the method Warré used for re-queening his hives. This information is paraphrased from pages 101-103 of the book.
It is best to perform this procedure in the early to mid spring (depending on your location). It may be performed some weeks after the hive has been enlarged but should be done before there are large numbers of drones present. Always perform this procedure on a nice day, preferably between the hours of 11am and 3pm. If you must re-queen the hive when there is a large drone population (summer), wait until 2pm, so that (hopefully) most of the drones will be out trying to mate.
In any breeding, introducing foreign blood is beneficial. Therefore, from time to time, you may want to introduce into your apiary a queen from elsewhere. In an apiary of between 30 and 40 hives, where selection has been made for several years, introducing new blood from elsewhere does not have the same advantage. An introduced queen is best given to a weak colony, or to one in which you suspect the desired genetics have not been maintained. In this way you only destroy an undesirable queen.
Once your new queen has arrived, place her in a quiet, comfortable and dark place; her cage remaining enclosed in the shipping box. If her introduction has to be delayed due to poor weather, the queen and her attendants can be kept in the cage for up to two weeks. Feed one drop of honey per day by placing it on the screen of the cage. This will keep the queen and the attendants alive and prevent them from consuming a large amount of the candy plug.
Before introducing your new queen, it will be necessary to locate and destroy the old queen. To find the queen in a People's Hive proceed as follows:
Remove the roof and quilt from the hive. Leave the screen in place over the top box. Lift all the occupied boxes off of the floor and set them off to one side. Break down the hive that has been set aside in order to determine which box contains the most bees, being sure to keep track of the order that all the boxes were in when you started. If it is difficult to determine which box has the most bees, select two boxes. On the hive floor, have or place one or two empty boxes; at least the same number as the number of boxes with bees you selected (these empty boxes may have already been in place). On top of the empty box(es), place a queen locator/excluder. Then, on top of the queen excluder, place the box(es) of bees. Smoke strongly and rapidly between the combs of the top box, driving the bees downward and through the excluder. When the bees have abandoned the top box, remove it and set it aside, proceeding in the same way with the next box if you have selected two. When the queen excluder is exposed the queen will be found, possibly amongst several drones. It is at this time that she is destroyed. Remove the queen excluder and stack the hive bodies, in the correct order, on top of the empty boxes which now contain the bees. Replace the screen, the quilt and the roof. Leave the hive for several hours.
Place the queen cage in the hive during the evening of the same day that you destroyed the old queen. Uncork the candy end of the cage, but do not make a tunnel through the candy. Placing the queen cage in the hive the same day should prevent the bees from making any queen cells. Return the hive to its original size, if necessary, by removing empty boxes from the bottom.