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The video above is great, here's a link to the Onc Click Root/Unroot files.
I will say, I had to drag the root.zip file myself over to the phone and rename it update.zip. I don't know why, but I had to do it manually. Then I clicked One Click Root and then followed the rest of the procedure to root the phone.
When I wanted to root easily, I used z4root. I think you can download it to your Captivate from the market, but you need to go into Flight Mode and then turn on Wifi to download it over a Wifi network, so you are not using the AT&T market that blocks the app.
The app doesn't require you to be connected to your computer to perform the root, which has a definite advantage over other ways of rooting.
EDIT: Seems that z4root was taken off the market since I last got it.