Much has change over the years in the way queens are installed. In the past beekeepers would find the queen they wanted to replace and crush her, leaving her at the entrance of the hive so all the bees knew she was dead and that it was time for the bees to accept a new queen. This process was wrong on so may levels and the practice is rarely ever done any more because attentive beekeepers noticed they were having trouble with new queen acceptance.
The present accepted practice is to find the queen you want to replace and remove the frame she is on and place her and the frame with some workers in a nuc box. A few other frames with brood and food will go in there as well. You do not kill the queen because she is your insurance policy. If your new queen fails, dies or is not accepted by colony you can reinstall the former queen into the hive and keep production going untill you can find another queen. Had you killed the old queen your hive could be queenless for a long while before finding another queen which could set off many disasters in the colony.
To install a new queen you will most likely have a wooden queen cage with a screen. Most often you will see a queen and five to seven attendant bees in the cage. Many people remove the attendants, but it is a better idea to leave them in there. Queens do not feed themselves and when you first get the queen cage you should place some sugar water on the screen. The attendants will feed themselves and the queen.
On one end of the wooden cage will be either solid wood or a cork. On the other end of the cage there will be white plug that looks like a marshmallow. This is a candy that one should run a pin or a small nail through. This lets the attendant bees know that this ia a way out of the cage, however you don't want them to get out too quickly because the smell of the new queen has to assimiluate the loyality of the colony. It is best to slow the queens exit by covering the candy on the outside of the cage with a piece of paper masking tape. This will slow the bees in the hive from eating through too quickly and killing the new queen before they accept her.
Once you poke a tiny hole in the candy end and cover it with paper masking tape you will set the cage between the top bars of two frames in the hive with the taped-over candy end facing upward. The screen should face down the isle between the frames for ventillation as opposed to pushing it into the wax.
Close the hive up and check on it the following day and each day after until you see the queen has been released. When she is out of the cage, remove and inspect the cage to make sure she is gone. If by chance she is still in the cage after four days you may release her into the hive. Once the queen is free in the hive, put the lid on and do not bother the have for at least ten day; longer if possible. Sometimes the bees seem to release the queen with some reservations and if the hive is disturbed too often they seem to blame it on the new queen and they could kill her.