Start with Rutherford. Look up his experiment and how he figured out that all the positive charge in the atom is concentrated in a tiny nucleus instead of being smeared out through the atom.
Rutherford went on to discover that this positive charge is due to the proton.
The neutron doesn't have a charge, so it doesn't affect charges the way protons do. So how was it discovered? That was due to James Chadwick, who was experimenting with radioactivity like Rutherford. He figured out that he was observing neutral particles and calculated what their mass had to be.
That should give you plenty to search on. You should probably get the details on both Chadwick's and Rutherford's experiments and the deductions from those.