At the time the AU was introduced, its actual value was very poorly known, but planetary distances in terms of AU could be determined from heliocentric geometry and the laws of planetary motion. Eventually the actual value of the AU was determined (approximately) from parallax observations, and more recently (and precisely) by radar.
Here are a few examples: Jupiter is 5.2 AU from the sun, and Pluto is 39.5 AU from the sun. The moon is 0.0026 AU from the earth.
Some approximate conversion factors:
See also: parsec and light year