Madrid has no single "downtown" station as such - Atocha in the south, for destinations in the south of Spain, Chamartin in the north, for destinations in....well, you get the picture. If you are joining the CF, I think you will be going via Chamartin. If you are arriving at Terminal 4 at Madrid airport, it has its own railway station on floor 1. Cercanias (suburban) line C-1 goes direct to Chamartin in less than 20 minutes. Fare is €2.60, tickets from a machine. (Have some euros ready.) Taxis, indeed! (Goes to lie down in darkened room.)