How does a ice skater spin fast?

By first spinning with the Arms extended, and then bringing the arms close to your body, you will spin faster.

This is due to the conservation of angular momentum and energy.

The equation for the amount of angular energy is (1/2)(I)(W^2)

I is inertia

W is angular velocity (pretend the W is lower case omega)

When you have your arms and legs out, You have an increased Inertia. According to the conservation of angular energy, your have to have just as much energy starting out as you do in the end. So, when you bring your arms and legs in, you increase your ending omega by decreasing you ending inertia.