The fastest way to get there is bus. There are buses from Krakow leaving from the Bus Station next to Main Railway Station on the upper deck of the station every 30 minutes. There are two major companies: Szwagropol and Voyager. Ticket costs 14 PLN and takes 1h 30min to get in.
As an alternative way, there are some trains from Krakow are around every two hours. It takes 2h 30min to get to Nowy Sącz. It's not very popular as it goes via Tarnów so it's good choice if you want to make a stop in Tarnow or see some landacapes.
The best way to get around the city and neighbouring areas is to use public transport system MPK Nowy Sącz. You can find timetables and search for connections online. If you use smartphone, for convenience sake there is an app Transportoid 2 available for iOS and Andtoid. So far this is the only mobile app that supports Nowy Sącz timetables.
Check the Nowy Sącz District Museum with several branches in different historical buildings.