Newton's third law is where it is at.
For every action there is an equal and opposite reaction.
If you're thinking of the standard triangular shaped aluminium foil ion "levitation" model, then DerStrom pretty much summed it up.
https://www.youtube.com/watch?v=71v5sFu7LT8&feature=related
In all ion engines a particle is given an electrical charge (the wire at the top) and it is then attracted to grid or a target which does not collect the particle.
The acceleration given to that particle is will give an equal and opposite acceleration to the ion engine.
In space the advantage of ion engines is that a LOT of energy can be given to even a single atom. Enough to push a starship.
If a single hydrogen atom is given a velocity extremely close to the speed of light, the assembler that accelerated it will recoil like a
high powered rifle shooting a tiny bullet, but on a much more extreme scale.
And this can also work in reverse. Decelerating particles can be used to generate electricity.
A really nice educational model is a Kelvin generator and they are very easy to build and safe enough for kids to play with.