How do you use potential energy to find velocity?

As Energy is a conservative Force, the total Energy of a system is the Potential Energy plus the Kinetic Energy.

In terms of gravity, the Potential Energy, U, is the mass of an object times the acceleration due to gravity times the height of the object: U = m * g * h.

The Kinetic Energy is one-half the mass of the object times the square of its velocity: K = 1/2 * m * v2

The equation, then, is E = U + K.

An example:

If an object of 50 kg is suspended, at rest, 100 m above Earth, the equation will be U + K = 0, since it is not moving. Then, to solve:

U + K = 0 => U = - K => m * g * h = - 1/2 * m * v2

the mass of the object will cancel, and we'll round gravity to 10 m/s2, giving us

10 m/s2 * 100 m = - 1/2 * v2 => - 2 * 1000 m2/s2 = v2

v2 = - 2000 m2/s2 => v = 44.72 m/s

The negative sign does not indicate a negative velocity, but the direction of the velocity vector, in this case, down.