Three kinds of "natural" Q/Cs.
Natural queen cells are distinctive and are built under three different impulses by the bees.
Supersedure, where the colony is trying to raise a queen to replace the one that is currently heading the colony. This could be due to age or damage. There are a small number, usually 1-3.
Swarm cells are built when the colony is preparing to swarm. They look similar to supersedure cells, but there are usually more of them.
Emergency cells are built on existing worker larvae when the queen is missing.
If queen cells are seen in a colony they are telling you something. Unless the beekeeper knows from the records of the previous inspection the reason should be investigated before taking any action. The cutting out of queen cells can be dangerous until you have worked out what is going on in the colony, otherwise you may leave it hopelessly queenless. I assess the situation when inspecting the brood frames on the way out, then take action on the way back.
The identification of the different kinds of queen cells is important, but easy to do. Supersedure and swarm cells are started on cell cups and are built as queen cells from the start. They will probably look similar and the only way of telling what they are is by the numbers - 1-3 will probably be supersedure, any more will be swarm. Emergency cells are built on existing worker larvae and are constructed differently, but there will usually be a break in egg laying, so making it easy.
The positions they will be found on the frames is often stated as supersedure on the face and swarm around the edge, but this is very unreliable and misleading - yet another of beekeeping's many myths. They can be found anywhere on the frame.
In assessing why there are unexpected queen cells in a colony you should be aware of the queen problems, as these are very common and you may be experiencing a failing queen, not what you may think.
If a colony is strong enough it will swarm on all kinds of queen cells, not just swarm cells. This is not understood by all beekeepers, but is the reason why many colonies swarm unexpectedly. In some instances they will swarm with a virgin queen.
When reducing queen cells it has become common in recent years for beekeepers to be told to leave two queen cells. The view being that if one fails then there is always another as insurance. This might appear sound thinking, but what happens if both queen cells are good? They are highly likely to swarm on the first one to emerge, which is probably what you are trying to avoid in the first place. In my experience swarms with virgin queens often settle much higher than those with fertile queens. I always advise only leaving one queen cell.
I mentally place my colonies into two groups, group "A" where I am happy to use queen cells from any colony and Group "B" where I am constantly looking to requeen. This is my way of improving my bees. If there are queen cells in a "B" colony I will probably cut one out surrounded by plenty of comb in case I need a queen cell later and destroy all the rest. If in an "A" colony I will cut several out with plenty of comb and will try to find a use for them.
In general you will only find one kind of queen cell in a colony, but there are occasions when you may find two. An example is when a colony is building swarm cells and you remove the queen. The bees will probably build emergency cells, especially if you cut out some of the swarm cells.
In recent years I have found both emergency and swarm cells in the same colonies. This is the bees being given different messages and I believe it may be connected to the queen problems.
When using queen cells be careful what you select. Assuming the cells come from good colonies you need to look quite carefully. Those of medium length (you will soon gain the experience after seeing a few) and heavily dimpled are usually good. Any that are smooth and/or long are usually poor, if indeed they contain a viable queen or pupa. If they are on the frame you will not usually be able to use them unless you cut some of the wood away as well, or take the frame with the cell on. When queen cells join it is virtually impossible to separate them because the web between them is so thin. On several occasions I have tried with a scalpel or razor blade, but I haven't been successful. It is better to pinch one out.
"Artificial" Q/Cs are produced as a result of the beekeeper manipulating a worker larva and encouraging a colony to convert it into a queen in some way. The notes above are equally applicable to artificial Q/Cs.