What are the two most common ways to produce hydrogen gas used in fuel cells?

Steam-methane reforming

Electrolysis of water

Explanation:

Steam methane reforming involves reaction of methane with water in the presence of a catalyst such as nickel to form Carbon oxides and Hydrogen.

CH4 + H2O ⇌ CO + 3 H

Electrolysis of water involves splitting of water through application of electric current to give Hydrogen and Oxygen gas.

2 H2O (l) → 2 H2 (g) + O2 (g)