the person or company that owns the rights to the song gets paid a small amount for each radio play, however, it isn't as simple as 1 play = 1 pay, because the companies that do the collection don't check the actual playlist of every station. they generally use several example station's lists, then collect accordingly from every station in that format, and distribute the money to the artists in question. ASCAP and BMI are the biggest companies that do this.
however, "artists" do not get the money. the songwriter gets the money, unless writing the song was a work for hire (i.e. you have signed a publishing deal with a company), or you have sold your rights outright to a publishing company. most big songwriters have publishing deals, that's how they get placed in commericals and sports arenas and things. so if linkin park does their own publishing, and has a hit song but only two of the members wrote the song, then only those 2 get paid.
but all that is seperate from radio PROMOTION. which, yes, basically comes down to paying the radio station to play your song. a good promoter can convince a station to play a song without money, especially if the artist is established. i highly doubt much money changed hands when U2's latest single came out, for instance. the station will play it because they KNOW it will be popular. but it's a given that any new artist you hear on the radio has had people bribing the station for them. clearchannel especially receives huge amounts of money from record companies.