Research catalytic chemistry. Catalysts affect reaction rate by lowering how much energy it takes to start a reaction. A constant amount of energy may produce hydrogen from seawater very inefficiently. Drop in a catalyst and the reaction may proceed very quickly. Seawater contains many impurities. These impurities may have a harmful effect on the intended hydrogen production. Catalysts have to withstand the chemical attack of seawater in order to be effective.
Use electrodes coated with manganese dioxide (MnO2). In principle, electrolysis is possible without the coating. However, uncoated electrodes quickly degrade. The UoS reference article explains why. Unwanted reactions involving sodium hypochlorite (NaClO) hinders hydrogen production. With the specially coated electrodes, seawater electrolysis gives hydrogen molecules with far less corrosive effects on the metal electrodes.
Utilize bacteria and/or plankton to expel hydrogen. Certain aquatic microorganisms expel hydrogen as a waste product. Growing and "harvesting" these organisms can aid attempts to extract hydrogen from seawater. If a friendly growth environment is present, the hydrogen-expelling bacteria can increase hydrogen supply over time. This trend is in contrast to "artificial" means such as electrolysis and catalyzed reactions. Fabricated chemicals and parts eventually wear out and degrade.
Calculate which production method (if any) may be commercially viable. New energy production has to compete with established names and brands, as with any industry or sector. Forbes Magazine has a flowery perspective on hydrogen in "Energy Revolution is Just Beginning". Nevertheless, the article makes a salient point: the hydrogen energy equivalent of a gallon of gasoline costs less than 50 cents as of July 2010. That is progress over previous research, especially on larger production size scales.