Before you attempt to install a new queen, make sure your hive has been queenless for at least 3 days. If your hive has a resident queen, remove and destroy her. Within a day or so of becoming queenless, your hive will probably begin to build queen cells (you may already have some in your hive if it has been queenless for some time, or your queen is failing). These should be destroyed before your new queen is introduced. You will be receiving your queen in either the 3-Hole cage or the California Mini Queen Cage (CMQ). If you install the queen too early the workers will most likely not accept her, and kill the new queen.
Remember the queens in the CMQ are alone and cannot survive without the workers outside the cages attending them; if you cannot install the queens right away, place them in a queen bank. And always keep your queens in a well-ventilated area, out of the sun.
CMQ with candy tube: The candy tube is designed to take 48 hours to chew through, and thus, allows 48 hours of introduction before your queen emerges (do NOT poke a hole in the candy, as it will cause the queen to release too early, and the workers will kill her). During this time the workers will become accustomed to the new queen.
CMQ with cork: This method does not include a pre-inserted candy tube. Before removing the cork, you should place your new queen in the hive with cork still inserted for a minimum of 48 hours. This allows the workers to become accustomed to her. After 48-72 hours, remove the cork and replace it with a bit of candy, granulated honey, or marshmallow. The workers will eat the candy, and the queen will release. Gradual introduction this way is generally better than directly releasing her into the hive.
Installing: Place the queencage between the center frames, with entrance side angling down about 45 degrees. The queencage can be placed about an inch from the top of the hive, unless you have very cold weather (in which case, place the queencage farther down in the hive so the cluster of bees can keep her warm).
After your hive has been queenless for sufficient time, remove the cork on the candy side of the cage (there will be a cork at each end but only one will have candy blocking it). You do not need to remove the worker bees from the queen cage. You'll probably need to remove one of the frames temporarily to fit the queencage in the hive. Place the cage about 1 inch from the top with the candy side about 45 degrees down, near the center of the hive.The workers will chew through the candy over a period of 48-72 hours and the queen will release.
Leave the hive undisturbed for a few days after installing the queen. Check to make sure she has left the queencage. If she is still in the cage it is safe to directly release her. The empty queencage can then be removed (and the frame replaced if you pulled one out). In about 4-8 days after she emerges, you should begin to see eggs. The time it takes for her to lay can vary depending upon the condition of the comb inside the hive and the weather.