To perform an ELISA test, scientists identify a protein that is specific to a particular disease pathogen, which is known to elicit an immune response - this protein is called an antigen. The antigen is bound to a test plate, and then the patient's blood is put on that plate to see if the patient has antibodies that will stick to the antigen.
After the antibodies have a chance to bind, the plate is washed off to remove any non-specific antibodies that did not stick to the antigen of interest. Then scientists examine the plate to see if any antibodies remain. If there are antibodies stuck to the plate, that usually indicates that the person being tested has been infected with the disease of interest. It is, however, sometimes possible that the bound antibodies were generated by exposure to another substance or disease and are simply cross-reacting with the antigen in question.
Fun Fact: The antibodies left on the plate are detected using specially-labeled antibodies that stick to antibodies! In other words, for the second part of the test, the patient's antibodies are the antigen.

