The following instructions are from the website of Olivarez Honey Bees.  Because we live in an area with aggressive feral honeybees, we would highly suggest that you use a beekeeping suit or at least a veil during this procedure.

Keep packages in a cool, shady, protected area with good ventilation. The bees should be clustered around the queen. If not, try to create a cluster again. Use your spray bottle to lightly spray through the screen onto the bees; they will gather again and hydrate themselves.

It is best to install your packages during the early evening hours, or during sunset. If you have to install earlier in the day, select a very shady area. This is for the protection of the new bees, and to prevent robbing, the entrances of the hives should be mostly closed. You can use tape or burlap leaving approximately two inches open.

To install each package, remove three center frames from the hive. Remove the feeding can from the package along with the queen. To keep the bees from flying, lightly spray the package with water before shaking the bees from the cage. Shake the bees into the hive. Give the bees 3–5 minutes to crawl up sufficiently so you can carefully replace the three frames. Now use the smoker using small puffs across the bees making them calmer and more manageable.

Check the queen. Pull cap off the plastic cage. Place the queen cage horizontally between the two center frames, one inch from the top, with the screen side down, so that the bees can continue to care for the queen through the screen until she is released.

If the bees start crawling over the top edges of the super, use a small amount of smoke and brush them back inside the hive and away from the edges of the super. Replace the lid and feed with sugar syrup, even if there is sufficient honey in the hive. The bees will settle and become more established before flying the next morning.

Check the colony in 5–7 days to make sure there are eggs and larvae and remove the empty queen cage. Keep them well fed for rapid buildup. As colony size increases be sure to remove the entrance blockage and boxes as needed.

Each beekeepers will develop their own method to install.  The following videos will give you insight to several methods to install packaged honeybees.