It is quite fast, with a train taking about 13 min. (4 stops from the airport) to the Main Train Station – Hauptbahnhof, or 6 stops to the Hauptwache which is the closest stop to the Römer and Altstadt. There is usually a train every 15 min. and they run from very early in the morning until quite late at night.
Use this website to find times, though it isn't really needed. www.rmv.de
Simply follow the signs to the Regional Train Station.
If you land at Terminal 2, simply take one of the free shuttle buses, or the Sky Train, which is a monorail that takes you to Terminal 1. It should take about 10-15 min. to go from Terminal 2 to the Regional train station.
Cost – a single ticket, one way (einzel Fahrt) costs 5.00 €. This ticket will take you into Frankfurt city center by train, and is also valid to get to your final destination by tram, bus, S-Bahn or U-Bahn, as long as you keep traveling without a break. An all-day ticket (Ganz Tag) for one person that includes travel to and from the airport as well as all public transportation in the city, is 9.75 €.