This is tested with Ubuntu Lucid (10.04), but I expect it should work with pretty much any system that uses Network Manager as the networking applet.
Tether your Captivate for Internet access over USB.
***NOTE: I'm too new to forums to post things that look like outside links, so a quick google of Cingular APN should get you the relevant user/pass combo you'll need in steps 8 and 9***
1. Put your Captivate in USB Debugging mode:
Settings > Applications > Development > select USB Debugging
2. Connect your phone to your computer.
3. Right-click on the Network Manager applet in your system tray, then click "Edit connections..."
4. Select the "Mobile Broadband" tab
5. Click "Add" -- your phone should auto-populate in the little drop-down menu to choose the device to use. I just left it alone and clicked "Forward"
6. Next it will ask you to confirm your location. If you're in the U.S., this will work. I'm not outside the U.S. at the moment, so I can't test anywhere else.
7. Select your provider. If you have a Captivate, chances are you're on AT&T, so pick that and click "Forward"
8. Next you need to pay attention or you may be paying $$$. In the drop down menu at the top, select "My plan is not listed" then fill out the APN info, and then click "forward" at the next window that pops up.
9. In the next screen it will autopopulate the "Default number" and then ask you for your username and password. The username is ATT/Cingular's info from the carrier file.
-- note the use of all caps in both places here. I don't know if it matters, but I know it worked in all caps. I left the other fields blank and left the other two tabs at default settings.
10. The setup is nearly done. Click "finish" or whatever it says on the last tab, and you're ready to rock. Disconnect from your WiFi (assuming you're testing this from home) and click Network Manager, connect to your new network (mine was named AT&T Connection 1. It hooks right up and runs.
The happy dance
There you go, 10 steps to free USB tethering with your Captivate, and all you need is a free OS and about 5 minutes. And yes, this was posted via a tethered Captivate.
I'm also working on getting Bluetooth tethering working, but it fails at the last step. Don't have time to figure it out tonight, but I'll give it another shot tomorrow after work.