Both the S8 and the S9 go from the Frankfurt Flughafen Regionalbahnhof to Frankfurt Hauptbahnhof. They both leave from track 1 (Regio 1). The direction (Richtung) will be either Offenbach or Hanau. Most of the S-Bahns go through the underground (tief) station at the Hbf; a few come into the ground level. If you go through the tief Bahnhof, you'll be underground with no visual reference, so watch for the name. It's the third station after the airport. The previous station is "Frankfurt Niederrad".
The Regionalbahnhof is under the bus building across the access road from Terminal 1. You can get to it via stairs from just inside the streetside wall of the main hall. If you come in on Lufthansa, or on some Alliance airlines, you will come into Terminal 1. Most US flag airlines use Terminal 2. If you come into Terminal 2 (D or E concourses), you will need to get to Terminal 1. There is a bus to Terminal 1 from outside Terminal 2, on the access road. You can also take the Skyline from the top floor of Terminal 2 to the top of Terminal 1. Follow the signs.
A single trip ticket (Einzelfahrkarte) for a single adult is €3,80. It will get you to the Hauptbahnhof and then to anywhere in the downtown area on any mode of transport, as long as you go directly there (no roundabout or backtracking). For unlimited rides in the downtown area after you get there, there is a Preisstufe 4 Gruppentageskarte, €14,30 for up to five people.