The Bastei is a popular tourist destination in the Saxon Switzerland. It offers spectacular views, many hiking trails start here and you can see the remains of an old medieval stronghold.
There are public buses that take you up to the Bastei from the surrounding towns. Another possibility is the Bastei-Kraxler, an old refurbished bus that takes you up from Wehlen during the summer month (first departure at the marketplace in Wehlen at 9:30am, from then every hour). The ride takes about 20 minutes and returns to Wehlen at the top of the hour from 10:00 to 17:00.
There is a transfer service on the street of Kurort Rathen. It operates a minivan to transfer travellers between Kurort Rathen and Bastei. After getting off the train, cross the river by boat. Follow the street and then you'll find the sign. No specific schedule. It departs when you need it. 12EUR/person. Not sure if it operates during the winter.
Follow the signs for Bastei, east from the town of Lohmen. Parking is 3 EUR. The walk from the lot to the bridge is about 10 minutes.