Usually most of poeple go to Hockenheimring by car. However you can also go there by train and on foot. Here is a map which way you should take from Hockenheim station to Hockenheimring.
Hockenheim bahnhof(station) is small, only one thing you can expect is kiosk. Taxi may be waiting in front of the station, but no more than 3 taxi even on DTM day.
You can eat and drink in down town of Hockenheim. Super market is also on the way to the circuit.
It takes about 40 minutes from the station to the circuit.
It would be great if this helps you.
View Route to Hockenheimring in a larger map