Frankfurt Airport: Skip the taxi unless you are loaded down or arriving very late. From Terminal 1’s Regionalbahnhof, take S8 or S9 toward Offenbach Ost/Hanau: about 15–20 minutes to Hauptbahnhof, or stay on for Hauptwache/Konstablerwache in the centre. The airport-to-city ticket is about €6.60. Terminal 2 adds roughly 15 minutes for the free SkyLine or shuttle to Terminal 1. For ICE/IC onward travel, use the separate Flughafen Fernbahnhof; local RMV tickets are not valid on those trains.
Frankfurt-Hahn Airport: Despite the name, this is not Frankfurt in any useful sense: it is roughly 90 minutes from central Frankfurt by road. The direct coach to Frankfurt Airport and Hauptbahnhof is the sensible connection, around €20.99 and roughly 90 minutes; allow a generous buffer. Do not book Hahn for a short Frankfurt break merely because the airfare is cheaper.
Frankfurt (Main) Hauptbahnhof: The main long-distance arrival point, west of the centre. For Altstadt, take U4/U5 to Dom/Römer or tram 11/12; for the river and Sachsenhausen, walk south or use tram/U-Bahn as appropriate. The station is huge and platforms are confusing—allow 10–15 minutes to find your train or connection. The immediate Bahnhofsviertel is useful for hotels and food, but not Frankfurt at its prettiest.
Frankfurt (Main) Südbahnhof: A useful arrival station for trains that bypass Hauptbahnhof and for Sachsenhausen/Museumsufer. It is connected by S-Bahn, U1/U2/U3/U8 and trams; walk downhill toward the Main for the museum embankment. Check your train carefully: many long-distance services call at either Hauptbahnhof or Südbahnhof, not both.