I was wondering how one would find what part of a protein is bound by antibodies in the body. I would assume it's not the entire protein but a certain amino acid portion, or am I incorrect?

It is indeed only a limited binding site, which is called an eptitope (and as a side note, while most common, antigens are not all proteins). There a range of options to identify epitopes, depending on what you start off with and what you want to figure out. They range from 3D analysis of high-resolution imaging of co-crystallized antigen-antibody complexes (which provides structural information but is costly and difficult and sometimes impossible to perform) to genetic methods. You will find more under the umbrella of epitope mapping.

Thank you!