Adaptive Immune Response and B Cells

B cells undergo a process of somatic recombination, where their genetic sequence (VDJ) is randomly recombined, ultimately leading to the production of an antigen receptor. The receptor goes through two stages of development within the bone marrow (negative selection: to prove that the recombination produced a "working" receptor that is capable of binding to an antigen; and positive selection: to prove that the B cell does not attack self-cells).

So, basically, it is random -- but that's sort of the beauty of it. Despite there being a limited number of genes available to the cell versus billions of potential antigens, the immune system is able to create receptors for things it doesn't even know exist yet. (T cells work similarly to B cells in their receptor production)

The B cells then encounter their matched antigen within the lymphoid tissues, again, a sort of random process on its own. But when they find it -- man, they're awesome at getting rid of it!   

It's a difficult process to summarize in a sentence. The B cell eats the antigen and through a process of clonal selection, it eventually finds the right receptor for the antigen. The B cell that finds the right receptor by guessing and checking matures. Here's a video on it:

https://biology-forums.com/index.php?action=gallery;sa=view;id=18520