In what episode does Roger find out about Jeannie? How does it occur?

Ahhh, an interesting ep. It was in episode #17, titled "Richest Astronaut in the World" (filmed on November 12, 1965 and released on January 15, 1966).

Basically, Roger just "accidentally" opened the bottle when Tony was not around, and out popped Jeannie, whom Roger happened to be looking for since he bumped into her and met her at the NAFSA base on a prior episode (and went out on a brief date with her too, I think). After opening the bottle and learning about her existence as a genie, he basically got greedy and stole her from Tony. Tony had to outsmart him to get Jeannie back.

HTH