The B3 from Hanover goes straight into the centre of town. Much of the Altstadt is a pedestrian zone, however, so you're better off parking at one of the car parks surrounding it. The Parkhaus Karstadt is a bit dingy but the all-day €4 parking fee is the cheapest in town.
Several trains each hour to Hanover take from 25 minutes (IC; €13) to 45 minutes (S-Bahn; €10). There are also IC services to Hamburg (€34, 1¼ hours).
To reach the centre from the train station, follow Bahnhofstrasse and turn left at the end of the street; it's a 1.2km walk.