|MadSci Network: Astronomy|
Assuming a knowledge of trigonometry, no telescopes or computers, you can measure the Sun's distance, but this method requires three steps:
Working out the size of the Earth
Working out the distance to the Moon
Measuring the angle between a half-Moon and the Sun
I can do no better than to suggest reading this site which explains how the Greeks did it, with technology no better than the Mayans. Although their results were only about 50% accurate, it's a remarkably good calculation of distances far beyond what they were used to in their daily lives.
Try the links in the MadSci Library for more information on Astronomy.