The capital, Leeuwarden, is easily reached by train from the south; trains can be caught from there to the coastal towns of the southwest, the port of Harlingen in the west and Groningen in the east. Note that the branch lines are run by Arriva, so if you're using an OV-chipkaart you must scan it separately from an NS train journey. For example, if you ride an NS train from Amsterdam to Sneek, at Leeuwarden you need to scan off on an NS machine, then scan on again on an Arriva machine for the branch line to Sneek.
The rest of the province requires more patience, but can be reached by bus or, in the case of the islands, by ferry; various day passes are available.
Cycle paths crisscross Friesland. National bike route LF3 bisects the province north and south through Leeuwarden; LF10 cuts across Waddenzee on the Afsluitdijk (30km) from Noord Holland and takes in the north Frisian coast and all the ferry ports; while LF22 covers the southern coast before heading inland towards Zwolle.