Here's a video demonstrating how to replace a broken blower motor resistor in a 2003 Chevy Astro van. I imagine the repair is similar for other vehicles.

Problem diagnosis: 1) Van would not start. 2) Charged battery and noticed that the blower motor was running even when keys were not in ignition. 3) Determined that the blower motor running must have drained the battery. 4) Read some forums online and decided the problem was likely the blower motor resistor. 5) Ordered the replacement part: ACDelco 8901 8436. 6) Made this video and everything works again!

I am not a mechanic but like to attempt my own repairs. I may overexplain things in this video but hopefully it helps you complete your own repair and save some $$.

Thanks to everyone else that has posted Astro Van repair videos, they've come in handy more than a few times!