How do electric and magnetic forces act on different objects?

It can push or pull an object ... I think.

Electric forces act on all electric charges, be those charges at rest, or moving. For static charges, the force is given by F=qE/kr^2 where E is the electric field, q is the charge, k is a known constant, and r is the separation of the charges. Magnetic fields act on moving electric charges, ususlly "seen" as forces acting on electric currents. This seems to be because a moving electric charge generates a magnetic field. That field would interact with another magnetic field to produce a force. As I remember it, a magnetic field would have no effect on a fixed electric charge.