This is a common misconception. (In fact, I think the New York Times ran an article about a British rocket enthusiast's dreams of using a rocket in space (back in the 1920's or so), saying that it wouldn't work for this very reason.)
1) Space is not a void. There's all kinds of plasma and other crap out there. This is not including the forces, like gravity, and electromagnetic radiation.
2) Use Newton's second law to understand. It says F=ma, which means that the force of an object is equal to its mass multiplied by its acceleration. Another way to look at this is that force is equal to the rate of change of the object's momentum.
Momentum, mass multiplied by velocity, includes a mass term. As mass is displaced, Newton's third law (equal and opposite reaction) assures a force in the opposite direction, because there is a change of momentum (thus, a rate of change of momentum).
So all you have to do in an ultra-low friction environment, such as between the Earth and the Moon, is kick out some stuff from the back.
What the Saturn V actually did (well, part of it), is power the astronauts out of the Earth's atmosphere, and then stop. They had enough momentum to just keep going (Newton's first law).