How do scientists discover a new antigen and its epitope?
Okay, you have a few questions building on top of each other (rephrased the questions for clarity):


  How do scientists discover a new antigen?


There are multiple ways to this, which are applied for different purposes.

In order to discover a natural antigen, which is recognised by an antibody normally produced by the immune system, one would first have get hold of this specific antibody. This would be an approach to reproduce or understand the effective response of the immune system against a pathogen (e.g. a virus).

In order to get hold of the antibody (and ideally the coding DNA sequence for it), researchers have to use the pathogen, or parts of it and find the antibodies (or B cells) that bind to it. To do this the pathogen (particles) could be fixed to a column and after running blood through the column the respective antibodies and B cells will remain in the column. Then the DNA of these cells can be sequences, or the antibody can be further purified.

In most cases however, scientists want to find a not-yet existing antibody against an antigen, which leads us to:


  Do scientists try to inject antigens to the body to see if it causes an immune response or not? 


Yes, this is done - but only with animals (mostly rats, rabbits &amp; goats). Polyclonal antibodies can be extracted directly from the blood of these animals, but most often monoclonal antibodies are needed for research or medical purposes. The process required for these is much more complicated, but leads to a cell lines which can then be used to produce the desired antibody in greater quantities.


  How do scientists know the corresponding epitope to an antibody?


There are multiple ways to find the exact epitope of an antibody, all of which are commonly described as epitope mapping.

The most common methods are based either on site-directed mutagenesis of the antigen to see which positions (amino acids) are crucial for binding of the antibody, or on peptide fragments of the antigen, which can still be bound by the antibody.