Meissen is 25km from Dresden and makes a natural day trip, though it is compact and pleasant enough to use as a base for exploring the Saxon Wine Route.
By train from Dresden: The S-Bahn line S1 runs from Dresden Hauptbahnhof to Meissen (Triebischtal) every 30 minutes, taking about 40 minutes. The more scenic approach is the historic steam railway (Dampfzug) that runs on certain days in summer along the Elbe; check the Sächsische Dampfschiffahrt website for dates.
By river boat: Sächsische Dampfschiffahrt runs paddle steamer services on the Elbe between Dresden and Meissen from May through September. The journey takes about two hours upstream, faster downstream. This is one of the more pleasant ways to approach Meissen — the silhouette of the castle and cathedral appearing above the river valley is striking.
By car: The B6 road follows the Elbe from Dresden to Meissen; the drive takes 30-40 minutes depending on traffic. Parking is available near the river and in several car parks in the town centre. The old town is compact and most sights are walkable from any parking area.