The old town of St. Gallen is almost void of traffic and is therefore best enjoyed on foot. The VBSG buses (http://www.vbsg.ch/) connect to the fringes of the city and run frequently and punctually. Bus tickets can be purchased at major bus stops or on the bus from the onboard vending machine. Standard fare is CHF 2.50 and is valid for one direction only. Taxis are always waiting at the train station and along the Marktplatz in the old town.
The Trogenerbahn (http://www.trogenerbahn.ch/) is your connection from St. Gallen to great hiking trails in Speicher and Trogen.
Bike rental is available at the train station, but check the opening hours before planning a trip.
By car
Parking is available underground in the Migros shopping center garage, near the train station. The garage is spacious and safe but like many things in Switzerland it closes on Sunday.