How do spacecraft use an orbit to move from planet to planet?

Any spacecraft sitting on a launch pad on Earth is already in orbit around the Sun because the Earth is orbiting around the Sun. We can put a spacecraft in orbit so it goes around the Sun the same way. From that point, the spacecraft can have its speed adjusted to change its orbit around the Sun. Those adjustments can take a craft to Mars or to Venus from Earth. This is called a Hohmann Transfer Orbit, or a least energy orbit, because this is the easiest way to send spacecraft between planets.

Basically, a spacecraft in a Hohmann Transfer Orbit is put into an irregular orbit around the Sun, with one part that is "lower" or closer to the Sun than the other. When a spacecraft is going to Mars, the spacecraft's perihelion (section closest to the Sun) will be Earth's orbit, and the aphelion (farthest distance from the Sun) will intercept the orbit of Mars at a single point. The spacecraft will change its orbit by speeding up with its thrusters. Spacecraft can go to Venus in the opposite way, with their "high" point, or aphelion at Earth, and their "low" point, or perihelion at Venus. This is done by slowing down through a retroburn, so the spacecraft can "fall" towards Venus.

Figures from NASA's Jet Propulsion Laboratory's publication: Basics of Space Flight Learner's Workbook. http://www-b.jpl.nasa.gov/basics/

After a brief acceleration or deceleration away from Earth, a spacecraft in a Hohmann Transfer Orbit simply coasts the rest of the way. Since the planets and Earth are always moving, getting to any other planet means that the spacecraft has to be sent away from Earth at the correct time to arrive at the other planet. This task might be compared to throwing a dart at a moving target. The opportunity to launch a spacecraft on such a transfer orbit to Mars occurs about every 25 months. Venus launch opportunities occur about every 19 months.

What is retroburning? What is aerobraking?
What could cause an orbit to fail?
What are the orbital lengths and distances of objects in our solar system?