Naumburg is a small town but it does have a very limited tourist tram service. Although I didn't witness a tram moving along the length of the track, it allegedly runs between the train station and Vogelwiess every twenty minutes throughout the summer (April-September). It operates between the hours of 2pm and 6pm, but only on the last weekend of every month.
Naumburg lies on the main Munich to Hamburg ICE line, and so is very easy to reach. It's about 30 minutes from Leipzig and two and a half hours from Berlin. There are also good regional services to towns and cities in Saxony-Anhalt, like Halle, and neighbouring states, like Weimar in Thuringia. The station is a little out of town, and walkinng into the city center will require you taking a look at the map that stands conveniently just outside the main exit.
Naumburg can easily be reached by car. Leave autobahn 9 at exit "Naumburg" and follow federal road 180.
Parking in the centre is quite cheap (50 cents/hour). If you do not shy a five minute walk you could park out of the centre for free.