My sister got into bee keeping a few years ago. She got in contact with a local beekeeper and he gave her lots of tips, plus a reading list. She now has 4-5 fully functional hives and sells local honey.
Usually, beekeepers will be ready for a new hive. Periodically, an established hive will split up (this is called "swarming"), with about 1/3 of the bees leaving with a new queen. They temporarily set up housekeeping in a tree, bush, or under the eaves of someone's house. The beekeeper is frequently called by the county* to remove them. At this stage they are quite docile; you can find pics of people moving them with bare hands, faces, etc.
There's a procedure to introduce them into their new home, the beekeeper can tell you what it is, it involves having at least 2 complete boxes IIRC.
BTW I'm told that if you encounter some "africanized" bees, you can tame them by replacing their queen with a domestic "un-africanized" bee queen.
*In many areas, it is actually illegal to kill a swarm of bees, so they are removed live.
DISCLAIMER: I am not a beekeeper, I'm passing along some of my sister's and brother's experiences.