Beekeeping (also called apiculture) is practiced by many farmers. The insects help to pollinate the crops as well as provide honeycomb, used to produce the sweet goodness of honey and beeswax for candles.
To start beekeeping, you'll need to get a beehive: a wooden box with a removable lid, some racks for the bees to put their honeycomb on and a small hole to allow the bees to get in and out. Once you have the hive, you need to get a queen and add the queen to the hive. The hive then needs to be placed outdoors and not too near any other hives. Hives that are too close together will compete for resources and none will do well. Beehives are permanent objects.
Once a hive with a queen is placed, it will hopefully attract a swarm of worker bees. Once the swarm has built up sufficently, they will begin to produce honeycomb. You may check the hive to ascertain the health of the queen, the size of the swarm and the prescence of honey.
In order to collect the honey, you will need a smokepot. The smokepot is a small pot which burns wood shavings. The smoke merely calms the bees down, allowing you to collect the honeycomb. It is still a good idea to wear some protective gear as you collect though, at a minimum a sturdy pair of gloves, a beekeeper's hat and an apron is recommended.
Note that some people are very allergic to bee stings. The first bee sting will generally give an indication of this condition, but later stings can easily prove fatal.