how do record companies make their money from radio stations?

Answer 1

They don't. They furnish the records free to the stations for them to play in the hopes people will like the songs and go out and buy the cd. If any money changes hands between a record company and a radio station, its the company paying the announcers to play a certain song. That's known as payola and its illegal.

Answer 2

"That's known as payola and its illegal." its sad because most of the record labels are still doing this—there are many many pending investigations into the major record labels. One label recently had to pay a fine of a few million dollars for a payola.