How fast do you move when riding a wave?

The average human runs about 6 to 8 mph depending on age, gender, fitness, and training. Average humans can sprint about 14 mph (well trained individuals run much faster). 
The speed of a breaking wave varies depending on the size and period of the particular wave energy; however, on average a wave moves about 10 to 15 mph. 
You ride waves about as fast as you can run but while standing on a hydroplaning board. Which is why the Beach Boys say "Catch a wave and you're sitting on top of the world".