Simple physics really. If you accept that F = GmM/rr and that if you integrate this formula to give an expression for the potential energy that needs to be overcome to get from the Earth to the moon, it's pretty big. But, most of that energy is used up getting into orbit. Once you're ina stable orbit, any noticeable impulse is going to send you out of orbit and off in whatever direction you were orbiting in plus a change depending on the direction of the impulse. Once you're in a frictionless environment and have escaped most of the gravitational pull of the earth, getting to the moon actually takes surprisingly little fuel.
On the way back, escaping the moon's gravitational field is simple as the gravity is much lower there. After that, point in the direction of earth and get a little speed, and you can use the earth's gravity to do most of the work for you, with some fuel used for simple course corrections.
Not too difficult really.