J.J Thomson came up with his plum pudding atomic theory after conducting experiments in 1897. He used a cathode ray tube to identify smaller than atomic size particles that were negatively charged. From this, he figured out that atoms were made up of both positive and negatively charged particles.
From his experiments, Thomson proposed that atoms make up of a positive mass with negative "corpuscles" (later called electrons), embedded in the positive mass, much the same as plums dotted in a plum pudding.
The plum pudding model was the theory of the day, until Ernest Rutherford--a former student of Thomson's--disproved it. He found, by experimentation with a different sort of particle beam, that atoms had a central positively charged core with electrons circling around the core.