How does the structure of an antibody adapt to recognize antigens?

OOH! My specialty! YAY!

Not sure what level of detail you're looking for, so I'll go basic- let me know if you need/want more detail.

Antibodies are produced by B-cells, in response to a specific antigen. Given that, I think your question may be a little off, because it sounds as if maybe you think that an antibody will change (adapt is the term you used) to suit other antigens. In reality, once it's made, it stays as-is, in many instances for the life of the organism.

Antibodies (immunoglobulins, or Ig for short) have at least four proteins: two heavy chains and two light chains. There are 5 different types of heavy chains: Gamma, Alpha, Mu, Epsilon and Delta, which are called by the first letter of their name, and give the name of the antibody (ab for short): IgG, IgA, IgM, IgE and IgD (an easy way to remember that is to think "GAMED"). There are two light chains, Kappa and Lambda. Every B-cell produces EITHER Kappa OR Lambda, but that's irrelevant for this question (but is a key feature of lymphoma and leukemia!).

Picture the letter "Y", which is what is formed by the interaction of the two heavy chains and the two light chains- the heavy chains join together to form the bottom of the "Y", the upper arms of the "Y" consist of the other half of the heavy chain wrapped around a light chain. The bottom of the "Y" is the Fc, or Crystaline (or constant) fragment, which is specific across species (every human has the same exact Fc as does every mouse, monkey, etc). The work happens at the top of the "Y", which is the Fab (antigen binding fragment). The B-cell will customize the Fab to suit the particular antigen encountered. Once secreted from the B-cell, there's no way for the body to make further changes to the structure, so it's programmed from the very beginning, kind of like old-school CD-R (write once) versus the newer CD-RW.