Marburg is easily accessible from Frankfurt by train. It takes about an hour. If there's more than one of you then the Hessen Länderticket could prove very good value. It covers you for travel all day on Frankfurt's metro system, all regional trains in the state, and all buses in Marburg. In fact for 31 euros it will take you anywhere on regional and urban transport all day in the state of Hesse.
If you have the money, or want to stop off in Marburg en route from North Germany, you can also visit Marburg via the super fast ICE train.
It's a real hike up to the palace, but lazy people like me are in luck: There's a bus. It runs every hour on weekends, and takes about 15 minutes to snake its way to the top around impossibly tight bends. The bus is small and supercharged, looking like it was built for trips in the Himalayas. It powers up the hill leaving more pedestrian cars in its wake.
You can pick up the bus by the fountain in the Marktplatz. If you travelled over from Frankfurt on the Hesse Länderticket, you can use that on this bus too.
Marburg is situated on the railway from Frankfurt to Kassel via Gießen, which is not an ICE route but still a major one. Trains from and to both Kassel and Frankfurt run once per hour, IC and RE alternating, and need about an hour to both ICE hubs. Local trains to Gießen and Treysa/Kassel operate in between. Secondary train routes lead to Bad Laasphe and to Frankenberg.
The train station was built in 1907/1908, substituting the plain brick station hall from 1850. The architecture is neo-baroque style with some Jugendstil elements. In World War II the station was heavily damaged and later rebuilt in a simplified shape.
The facades have been done recently but the interior and the platforms are in need of a renovation.
The buses into town depart from the stop on the opposite side of the square. If you want to walk, the way to Elisabethkirche takes about 10 minutes on foot.
Public transport in Marburg is done by buses. The bus network has never been good and my latest visit, seven years after moving away, showed me it has not notably improved. On the main routes in town - most buses run more or less the same route in the centre - you can get along. You also reach the suburbs but buses run only twice per hour and line, a few lines three times per hour in the daytime, less in the evening and on weekends. Bus connections to the villages beyond the hills are a nuisance.
Expect buses from/to the train station and the centre to be very crowded, as they are used by many many students and there are simply not enough buses. Besides, the timetable is a mess - often you wait for 15 minutes and then you have three or five buses coming within a minute or two. There is also a bus line (16) through Oberstadt up to the Schloss which might be useful but this one runs just once per hour...
Conclusion: If you want to visit no more than the town centre and train station and don't have much luggage, better walk.
Timetables, fares etc. on Stadtwerke Marburg website (in German).
Marburg is part of the RMV Verkehrsverbund, all information can also be found via the RMV website (in English).
The ascent to the old town is steepest from Pilgrimstein and Rudolphsplatz where the hillside is almost vertical. To make reaching the Oberstadt easier, around 1990 the town built a lift here which saves a bit of climbing. At the top you end up in Wettergasse, a few steps from market square.
The lift operates from 7 a.m. in the morning to 1.30 a.m. at night. The use is free.
Bottom: Pilgrimstein, corner Rudolphsplatz, opposite of the Sorat Hotel and next to the tourist information.
Top: Wettergasse, next to Elwert book store through a narrow passage - watch for the sign "Oberstadt-Aufzug".
Yes, sightseeing in Marburg involves a lot of walking. But there is good news: three elevators make it easy to make shortcuts uphill or downhill. All three elevators are located in the street Pilgrimstein, which is at the bottom of the steepest castle hill part in the east (see screenshot google maps, photo 4). The northern one is part of Parkhaus Oberstadt (parking old town), no. 1 in my screenshot. This one reaches the old town at the place where the statue of Christian is, next to Café Klingelhöfer. The other one is actually two paralell elevators, called Aufzug Oberstadt and they are located at the southern end of Pilgrimstein (street), opposite of the Best Western Hotel (signs see main photo, no 2 in my screenshot). They hold approx. 10 people each. They arrive in the old town in Reitgasse, next to the bookshop Elwert. And the other one is the one which connects the upper and lower part of bookshop Elwert (no 3 in my screenshot).
Of course these elevators are free of charge. They are big enough for pushchairs and wheelchairs. They operate from 6:30 in the morning until 1:30 in the night.
As a university city, Marburg is very much student friendly and this includes that the city gives bicycles a very high priority. The bicycle lanes are real ones, separated from the car traffic and no one needs to fear to get killed by drivers with an overly “Michael Schuhmacher” attitude. Even the traffic lights for pedestrians include the icon for cyclists.
Especially for Don and everyone who arrives by train and would like to rent a bike in Marburg: bike rentals are at the train station. Rental fees are 6 € from Monday to Thursday and 7,50 € from Friday to Sunday. It is allowed to take the bikes on busses, however off-peak hours only.
Marburg has excellent train connections to Frankfurt. Every hour an IC (Intercity) train stops here and every hour a regional train. Most conveniently these trains leave/arrive in intervals of 30 minutes and both trains need approximately one hour.
In case you arrive by train from a distance of more than 100 km, the train ticket includes the city option, which means you can take a bus to and from your final destination without buying an extra bus ticket.
Marburg’s bus service is excellent! Each single ticket is 1,50 € for adults and 0,90 € for kids. Day tickets are available for 5,95 € and include five passengers, which is ideal for families with kids. In addition, there is a so-called shopping ticket available, for 3,15 € unlimited bus travels per day within “Marburg Mitte” (but this includes Lahnberge).
See bus map for details about bus lines and stops. The website below is a pdf with prices, albeit in German only.
Marburg is about an hour from Frankfurt. There are direct trains, but some also stop in Giessen. Listen carefully to see if you need to change. It costs about 11 euro from Frankfurt (one-way). Trains leave pretty much once an hour.
Marburg's train station is just north of the old city.