To propel a spacecraft, due to the law of conservation of momentum, if you want to go in one direction, you have to push something (the propellant) in the opposite direction.
It's the momentum of the ejected stuff (mass*velocity) that matters for maneuvering in space. You have to carry that propellant with you and accelerate it. You can use specific impulse to compare efficiency of rockets (the higher, the more efficient is the rocket in creating forward thrust with the same amount of propellant). The best engines we have are ion thrusters because we can accelerate a small amount of gaz (not very heavy to carry) very fast => big momentum. But thrust is limited, this why you can not lift off from Earth with an ion thruster.
Nuclear energy is just used to power spacecrafts in electricity when you can't use solar panels.