How do unbalanced forces affect an object's speed?

Newton's Laws of Motion tell us that the velocity of a body remains constant unless subject to a force. If there are more than one force acting, it will be the net force that causes any change in velocity. So in the case where the forces are balanced, nothing will change, but note you must be sure the forces are balanced in direction as well as magnitude. In fact what you have to do is evaluate the net force as a vector quantity. If the forces are in fact unbalanced this means there is a net force in a certain direction, and this will act on the body, in that direction. (Force = mass x acceleration)