The red train crossing the bridge in this photo is the S8, which has come from Hanau by way of Frankfurt and the Frankfurt airport.
From here it will go on to Mainz Süd (south station), Mainz Hauptbahnhof (central station) and from there to Mainz Nord (north station) before crossing back over the Rhine on another bridge in the direction of Wiesbaden.
You can take your bicycle for free on the S-Bahn in the Rhine-Main area, but you must have a ticket for yourself before boarding the train.
The S-Bahn trains are the only ones that stop at each and every stop along the way, and they are the only trains with no toilets, on the theory that people will use them for short rides only.
Mainz, being close to Frankfurt, has excellent train connections, plus a number of direct lines from the city itself to numerous destinations about the country. From Mainz Hbf you can get direct trains to Hamburg, Cologne, Stuttgart and even Innsbruck and other cities in Austria. The station is located on the western edge of the old town, and if you want to get into the main part of the city as fast as possible its best to take a right up Bahnhofstrasse and head towards Schillerplatz.
S-Bahn or RE trains from Frankfurt takes about 45mins to 1 hour to Mainz Haupbahnhof. The Mainz suedbahnhof is nearer to the centre of the town though. About 5-10 mins walk from Mainz suedbahnhof.
S-Bahn trains also run into the nearby towns such as Wiesbaden in less than 10mins.
From the Frankfurt airport, it's easy to visit Mainz since there's a train station inside the airport. The train will have visiters in Mainz within fifteen or thirty minutes, depending on which train they ride. However, there's more than one station for Mainz, so be sure to depart at either the Mainz Main station or the Mainz Sud (south) station. Don't depart at the Mainz Kastel station, which is abandoned.
By far the best way to get around Germany is by train. Rail service is suburb even though it is a little expensive. Trains run to/from Cologne every hour and stop in Mainz on the way. You can also catch trains from Koblenz to Mainz or Frankfurt which will lead you by the Rhine river for most of the journey.
Mainz is well connected with Wiesbaden and Frankfurt through the S8 suburban railway line. Trains run every half an hour with a night break lasting only from around 1 am to 4 am. The trains coming from Frankfurt also stop at Frankfurt Airport (usually track 3). Single tickets are 7,80 EUR from/to Frankfurt Hbf (central train station), 4,35 EUR from/to the airport and 2,60 EUR from/to Wiesbaden (all prices for adults as of late 2013). Day tickets are double the price which means that they cost the same as two single tickets and are worth to buy for return trips. Tickets from Frankfurt or Frankfurt Airport to Mainz also includes Wiesbaden. There are ticket machines at every station.
There are two important stations in Mainz' city centre, Hauptbahnhof (central railway station) and Römisches Theater (locals often call it Südbahnhof which was its old name until 2006). Both are equidistant to the pedestrian zone around the Cathedral. Hauptbahnhof has more connections to other destinations and is handy for sights in the Northwest of the city (like Christuskirche and the new synagogue) while Römisches Theater is closer to the Zitadelle, Kupferbergterrasse and places in the Southeast of the old town.
Be sure that you take the S8 as the other S-Bahn - trains going from Frankfurt to Wiesbaden (S1 and S9) do not stop in Mainz. Only if you are really desperate, you can take the S9 and get out at Kastel (often called Mainz-Kastel, though this place belongs to Wiesbaden since the end of WWII). From there buses run to the old town in Mainz or you can cross the Rhine bridge which is a 15-20 minute walk.
Best deal is to get a German Rail Pass which allows unlimited travel for a given days. Train tickets are not so cheap in Germany. To see the beautiful Rhine Town and Castle, you need to use the train to get to places like Bingen, Koblenz and St. Goar
PLEASE NOTE THAT FERRY DO NOT RUN OR ARE VERY LIMITED DURING WINTER TIME SO TRAIN IS A MUST IN WINTER
The bahnhof is located in the centre of the town which is about 15 minutes walk from the Market Place.
You might also want to consider getting a Rail pass from Traveldex which offers cheap rates for oversea visitors
There are frequent trains that run between Mainz and Frankfurt - with a convenient stop at the Frankfurt International Airport. The only trick is making sure that you board the right train - there are several platforms - and you have to make sure that you're on the right portion of the platform.
The Hauptbahnhof in Mainz looks more like an impressive civic museum than a train station!