With the train it takes approximately 30 minutes from Vienna to Baden. One ticket at regular price and per direction costs approx. 5,50 Euro. You can find the details to the stops and the timetable under following link: ÖBB Timetable
Tip:You can find the railroad track and the locations of the different stations at the Interactive Map. Just choose at the map "Public Traffic".
The railway station of Baden is not directly in the town center but in walking distance. When you leave the railway station at the main entrance just cross the street to reach a small park. Go straight ahead on the main path till you reach the end of the park. Now cross a street on the zebra crossing to reach the alley Bahngasse. At the end of Bahngasse turn to the right into Wassergasse. You can find this crossing on the town center map in the square E1.