Some simple ways
It is reasonable to assume the beginner probably only has one colony and little experience of beekeeping. In their first year or two they are probably more likely to have higher losses than more experienced beekeepers, which is one of the reasons why I advise all beginners to have two colonies as quickly as they can. If they lose one, they should still have the other one from which to make increase.
I strongly advise beginners against buying bees, unless from local sources, where often other beekeepers have a surplus. You will learn far more by making your own increase, not only about how to make the increase, but basic queen rearing too. There is a lot of satisfaction in producing your own colony, especially if you have had a hand in rearing the queen that heads it. Any learning, especially at an early stage is well worth experiencing.
Some of the normal methods of making increase may seem complicated for the beginner, probably the main reason why there is often a reluctance to make their own increase. This page is designed to help the beginner increase their number of colonies or make up losses by using simple methods only. I have tried to reduce some of the problems, which are known to experienced beekeepers, but may not always seem obvious to a beginner. The more experienced beekeeper and more advanced methods avoid these, but probably by using ways that may seem complicated to a beginner. There may be those who will say "what is he advising that for?", but I think it's important for beginners to be successful. When they have gained enough experience and knowledge they can use the more conventional methods.
I believe that all beekeepers need to know what I call the "basics" of beekeeping at a very early stage. Without them you are going to struggle to manage your first colony properly without it misbehaving. In particular you need to be able to find queens, know the life cycle of the queen, the swarming procedure and what happens in a colony when the queen has been removed.
There is a lot of sound information on this website to help you. Below I highlight a few points you need to be aware of:-
I will assume the beginner has one full colony and they wish to make increase of one new colony. I will offer several options, but please don't try to mix anything. Try to understand what is happening at each stage and how a normal colony progresses during the summer.
You will need some sort of hive to put your new colony into. Temporarily this could be a nuc box, especially if you are going to move it away for a short time, but you will need a hive at some time. You can make the hive and frames up, but don't put any foundation in the frames until you need to, otherwise it will go stale and the bees may not build comb properly.
You will also need a queen or queen cell. In both cases you need to know how to introduce them to reduce failure. If a queen cell is used, then protect it if you are introducing it on the same day. An unprotected queen cell should be O.K. to introduce the following day. You may need to remove emergency cells 3 days later. I strongly advise against buying a queen. If they come from a commercial source there is a fair chance they may be imported, running the risk of importing pests and diseases we haven't got and it is unlikely they will be best suited to our conditions. During the summer there are usually plenty of queens and queen cells available. Just ask your local BKA members.
I have put buttons to relevant pages on the top left, rather than as highlights throughout the text. In reading the pages you may need to select the information you require.
I have suggested moving bees away for a short time. Three weeks is usually enough, before bringing them back. As a beekeeper it is always worth having an alternative site that can be used on a temporary basis. This could be a non-beekeeper or another beekeeper. Make sure the bees aren't a nuisance.
Option 1. Swarm.
I see absolutely no harm in making increase from a swarm. Make it known in your BKA that you would like a swarm and offer to help collect it if you haven't done it before. Sometimes a little knowledge is needed. Don't be put off by those who give dire warnings about the "dangers" of swarms. You can learn a lot and in my view this far outweighs any perceived problems. All the so-called problems with swarms can be relevant when acquiring bees on combs too.
There is one downside and that is you don't know when a swarm is going to appear, but if you haven't got one by, say, the end of June, then you can always split your existing colony.
Option 2. "2 Frame Nuc", but moving off site.
Make a "2 Frame Nuc" as described on the page. Make sure the queen is left behind in the parent colony. If there is a nectar flow a strong colony will recover very quickly and the removal of a small nuc, especially early in the season, should not reduce the honey crop.
If the frame of brood is well covered with bees there is no need to add any more. You should be aware that frames of food have far fewer bees covering them than frames of brood do. If your nuc is a bit short of bees, then shake a comb of bees into the box. Add foundation (or comb if you have it). Close up and move 3 miles or more away. Give a queen or queen cell when it is set down.
Option 3. Modified "Artificial Swarm".
Move the parent colony to a new position. In its place put a fresh hive with brood box only. Remove one or two frames of brood and one frame of food, all with adhering bees, from the parent colony and place in the new hive. Fill up with foundation and close up. It is better if the queen stays in the parent colony. Leave any supers with the parent colony. Give a queen or preferably a queen cell to the new colony.
There are a number of other ways of creating increase, but until you get fairly proficient I would stick with these simple methods. If you have any problems they can soon be dealt with and I have deliberately used methods where there is little cost.
In all the options above I have assumed there are no active queen cells. If there are, and the colony is reasonably docile, then you can use the queen cells. Don't forget that you will need to deal with these, otherwise you may have a swarm.
An experienced beekeeper, when making increase, will probably use the opportunity to improve their bees. As a beginner I don't think you need bother about that, unless you have an aggressive colony, until you have a bit more experience.
If you make your increase towards the end of the season you can bolster the smaller colony by giving it a comb of largely sealed brood, without bees, every 7-10 days from your other colony. The removal of brood won't reduce the foraging force, because in normal circumstances an egg doesn't become a foraging bee for 6 weeks.