But first, just a very simple biology lesson of hair itself. The individual strand of hair that we can see popping up above the skin is usually referred to as the shaft. The hair below the skin is usually referred to as the root. This root is encased in what is known as the hair follicle. Within the root, there exists many types of cells with many different functions. There is one grouping of cell/cells, whose function is to make a new hair. For simplicity sake, I will label these cells as the "propagating set".

So, a hair is removed, and a "propagating set" is derived from it. This propagating set of cells is sent to a laboratory, where it is grown in a medium, that allows it to make all kinds of little babies, so eventually, there are all kinds of little propagating sets swimming about. These sets are then returned back to the person performing the procedure, and then placed back into the scalp, where many hairs can then begin to grow.

At this point, an injection method seems to be the most likely scenario, so that these cells are injected back into the scalp with some special syringe-like tool. However, a more traditional transplant method is also a possibility, at least until an injection method is devised. It is also unclear as to whether this procedure can induce new follicles to grow, or whether it simply stimulates existing follicles, but the consensus of opinion at this time, is that even if new follicles can not be recreated now, it is likely that there will be a method to do so eventually.

As you can see, the method used is completely speculative, since no one has delivered a working procedure yet. And it is quite likely that hair multiplication may simultaneously consist of multiple methods, as each researcher improves upon the preceding methods with his own fine tunings.