Water molecules are made from two atoms of hydrogen and one atom of oxygen. You can use a process called "electrolysis" to separate the hydrogen and oxygen atoms in water. Electric current is passed through water, causing the water molecules to split at the atomic level.

Industrial Electrolysis

Sometimes, electrolysis is used to create very pure qualities of hydrogen for use in industry. The resulting hydrogen is sometimes used in hydrogen torches and could theoretically be used in hydrogen fuel cell vehicles.

Electrolysis at Home

You can also perform electrolysis at home using just a few household items. All you have to do is run electricity through water that has been mixed with some kind of electrolyte (common table salt is a great example). One common way to build a homemade electrolysis unit is to run electric current into two pencils resting in a glass of salt water. If you want to build this type of unit, get together the following materials: a battery of some sort (preferably a nine-volt), two eraser-less pencils, a small cutout of poster board, a glass, some wire and salt water. Fill the glass with salt water and place your poster board over the top. Now, making sure that your pencils are sharpened at both ends, push them through the poster board so that they are sticking into the water. Cut your wire into two sections. Wrap one of the wires to each pencil and connect the other ends to the positive and negative charges on the battery. As the electricity passes into the water, very small bubbles will begin to form around the submerged ends of the pencils. The gas gathering near the positive charge is oxygen, and the gas gathering next to the negative charge is hydrogen.

Source:

TAMU.edu: What is the composition of water?

ReachoutMichigan.org: Splitting Water