Lets first take a quick look at How do you split atoms? The short answer to this is that you take unstable atoms and fire particles at them. If a particle hits the nucleus of an unstable atom, the nucleus breaks apart into smaller pieces, releasing particles and energy.

Some isotopes of atoms, especially heavy ones, are inherently unstable. When struck with a neutron, they break apart, releasing energy and more neutrons. These more neutrons can break up other atoms of the same kind, releasing more energy. This is called 'nuclear fission', and it powers both nuclear power plants and more primitive nuclear bombs.

For more information, take a look at:
The ABCs of Nuclear Science
ABC of nuclear power

Hope this is helpful.