As Kate Hardy asked, I will do my best to explain. We have been keeping bees since 2000, so are not as expert as some people but here goes:
The best place to get beekeeping equipment is Thorne (Beehives). They are one of the premier beekeeping suppliers in the world and are located in Linconshire. They also have all manner of candle making equipment as one of by product of bees is wax. And pound for pound, beeswax is more expensivethan honey.
The best book on beekeeping is probably Ted Hooper. Guide to Bees and Honey ISBN 1899296042
For a more American approach there is Sammataro and Avitabile The Beekeeper's Handbook 0801485037
A bee hive consists of a stand, a floor, a brood box ( this is where the queen lays her eggs and is made up of approx 13 deep frames) a a crown board and a roof. When you are trying to collect honey, you add a queen excluder and supers (boxes filled with frames that are half the width of the brood box frames) The main reasons for keeping the queen out of the suppers are bees arevery reluclant to leave the brood nest, and successive hatching of bees means a build up exoskeltons, turning the frame wax black. You always have to take the impurioties out of beeswax and the wax from the honey cappings is the most higly rpized as it is nearly white. When honey is ready -- the bees put a wax cap on top of the honey in order to keep the honey in storgae.
The harvesting of honey can be done in many ways. The simplest is through the use of a crown board and Porter bee escapes. The bee escapes are little plastic devices that allow the bees to exit the super but not re-enter. It the bees think the honey is inaccessible, they will try to move it to another place and can rapidly empty a super. The theory is: you put the Porter bee escapes in place, and leave the super to clear of bees. When you return, you pick up the super, put a cloth over it to keep out any interested bbes and take it off to some place which is a bee free zone to extract the honey.
As it anything, if you have the right tools for the job -- honey extraction is pretty stright forward. We use a centrifugal force extractor as we only have (in theory) two hives. Larger commerical operations have electrical extractors. You first extract the honey, then you put the honey in a filter tank to get rid of most the impurities (like the odd dead bee) and then you can bottle the honey. Everything gets sticky, but it is satisfying and the children get rather sick on chewing beeswax cappings as they are still full of honey. Some people wash the cappingss and use the water to make mead. Other people feed the cappings back to the bees. The bees turn the cappings over and over, cleaning them of honey, and then after a few days, the beekeeper collects the cappings which can then be melted down. Beeswax smells wonderful.
Swarms occur when a colony gets overcrowded. beekeepers spend a lot of time and energy trying to prevent swarms. As the loss of a swarm means less honey. There are many theories on how to prevent swarms, but really if the bees have made up their minds, they will swarm, they swarm. To capture a swarm (and it needs to be on your property/you must have permission of the property's owner/you must have seen the bees exit your hive) you need either a skep or a stout box or other device for catching swarms (Thornes have something that looks like a canvas bag attached to a pole. When bees first exit the hive in a swarm, they are fairly dolcile as they have engorged themselves with honey. After a few days, they are starving and so are less easy to handle. Bees have a nautral instinct to move upwards into a dark place as they naturally like to build hives in tree holes. When they first leave the hive, the swarm lights on a branch while scouts look for a suitable place to build a new hive. The beekeepers captures the hive either by knocking the bulk of the swarm in to the skep and placing the skep upside down a board on the ground below the tree with a slight tilt in the bottom to allow the bees to enter and exit. Or the beekeeper positions the skep over the swarm and hopes they will move up. In either case, the beekeeper then waits for dusk when the bees are clustered inside the skep. The beekeeper then moves the skep on top of the board (having made sure the bottom of the skep is now flush with the board to the empty hive. The beekeeper then raises the board to a 45 degree angle with the ground and the entrance to the hive, gives the skep a smart shake and the bees tumble out of the skep on to the board. The bees start to move upward into the new hive, sometimes assisted by the use of smoke. It is amazing to watch.