How long can they experience zero gravity at a time? So, what altitude do they start at? What profile does the airplane take? How fast does the airplane get?
What kind of airplanes do they use? How much does it cost? What companies provide this service? Where does the FAA allow this? Does anyone use this for anything other than training astronauts or making tv/film productions?
Space Adventures arranges zero-G flights on Russian aircraft. Their home page should answer your other questions. There’s also an American company called Zero-G which offers (or plans to offer) zero-G flights using a Boeing 727.