The hydrodynamics of a surfboard are very important and also very complicated.  There are many variables on a surfboard that affect speed, stability and maneuverability.  These variables include friction, form, and fins. 

Friction, or drag, has a large impact on speed.  Even the slightest roughness such as scabs of wax on the bottom of the board can make the difference in avoiding a wipe out.  These small imperfections cause enough friction with the water that a turbulent flow results, decreasing speed. 

Several characteristics come into play when form is considered, such as rocker and rail shape.  The rocker (curve on the bottom of the board) needs to be just right for the board to plane ideally.  Too much rocker will cause the board to drag decreasing speed.  Too little rocker will leave the tip of the board prone to catching, resulting in a head first wipeout.  Rail shape affects the lift (pressure distribution on the water) of the board which allows for hydroplaning.  Tail shape also affects speed.  A v-shaped tail reduces the friction that results from the turbulence of the board moving across the water. 

The hydrodynamics of fins gets very complicated.  Simply put, the fins apply the torque applied by the rider to the water allowing the board to turn.  The fins act as a lever.  There is an optimum point where maximum speed and maximum maneuverability are obtained.  

Surfboards are almost always hand shaped.  There is a great deal of knowledge and skill required to build a fast yet maneuverable board.  Surfing experience and science play an equal role in this process. 

The following diagram shows how complicated the analysis of water flow around the board becomes (from Surfboard Hydrodynamics Part 1: Drag by Terry Hendricks Ph.D.)