In order to travel from Earth to Jupiter, you can imagine just pointing your spacecraft at Jupiter, firing the rockets until you've arrived. Although this would work if you had an incredibly powerful rocket, and unlimited fuel, that might work, but it's not really feasible for our current technology.
In order to get to another planet in the Solar System, engineers use a method called Hohmann transfer orbits, which allows you to travel from planet to planet with the least amount of fuel.
For starters, consider that a spacecraft is already going the velocity of the Earth orbiting around the Sun - just sitting on the launch pad. All it has to do is escape the gravity of Earth, and then change its orbital speed around the Sun so that it's going the same speed as Jupiter.
NASA's Galileo spacecraft was originally supposed to take only 2 years to reach Jupiter following a direct flight path. It was supposed to launch from the space shuttle Challenger, but after the disaster, NASA decided to give it a slower route that involved several gravitational flybys around Venus and Earth. In the end, it took about 6 years to reach Jupiter.
NASA's New Horizons spacecraft, the fastest spacecraft ever launched, took just 13 months to reach Jupiter from Earth. It will reach Pluto in 2015.