Eppingen is located on the tram respective S-Bahn line S 4 from Karlsruhe station and city centre via Bretten to Heilbronn. Eppingen is the last stop within the KVV network, the rest of the line further north belongs to the VRN network. So check which tickets you need, depending on direction and destination. Trams run at least twice per hour in the daytime.
Having a closer look at the timetable is recommended. There are different types of trams. The normal S4 stops everywhere. Those marked "Eilzug" (express) stop only at the major stops, hence they are faster. Every two hours there is also a "Kraichgau Sprinter" which is the fastest but stops only in Bretten, Durlach station and Karlsruhe central station; unlike the first two it does NOT go through the city centre of Karlsruhe.
KVV timetable information (in German only)
VRN website (click the flag for your preferred language)
From Eppingen station it is a few minutes walk into the centre. You see the old town and its 'skyline' from the station, to miss it you'd have to try very hard;-) The most interesting walk is through the park and over the small wooden bridge, then along Fachwerkpfad with the models and explanations about timberframe architecture (see Things to do tips).
Eppingen is a part of three commuter travel areas (Verkehrsverbund)
It's part of the Karlsruher Verkehrsverbund (KVV), Rhein Neckar Verkehrsverbund (RNV) and Heilbronner Nahverkehrsverbund (HNV) and it is not far awar from the Stuttgarter Verkehrsverbund.
Depending on where you want to go, it is a good idea to buy 24h tickets instead of single tickets. Most of the ticket vending machines are multi lingual.