This LAT article gives an excellent recap of the physical demands of the sport of surfing. Like most other physically demanding sports, training outside of the actual practictioning of the sport is vital. The author cites push ups, sit ups, swimming laps and running up sand dunes as good conditioners for the actual sport. Failure to be in good shape can be a life risking experience as surfers can drown if they become exhausted.
While surfing can be particularly dangerous because of the risk of drowning, physical conditioning is vital for all serious sports. Your skiing, surfing, mountain climbing, wind surfing activities will all benefit from an active program of functional training that strengthens the core.
There is a typical core exercise routine that has obvious implications for improving your strength and balance for surfing as well as other sports. While the exercise focuses on the triceps, note the total core engagement and balancing being accomplished at the same time.