The Samsung Captivate is very simple to root and install a custom ROM. I would recommend you remove your external SD card before doing all of this as a precaution. The steps don't involve formatting it, but I would hate to lose all my stuff on my external SD. The interal SD may be formatted and you will lose all apps and data on there as well as the system data, BACK EVERYTHING UP before you start. For PC backup I have used Wondershare MobileGo, it worked great for me. I am on Windows 7, all the apps and files here work using this system (sorry Mac and Linux).
Prerequisites
The Captivate has an internal SD and external SD, when copying files in this guide they go to the Internal SD card. It might work from external, but for simplicity use the internal. If you have any program errors you may need to install the Microsft Visual C++ redistributable pack in the downloads below. Install that then try again if you have any issues.
Downloads:
ClockworkMod Recovery - http://www.megaupload.com/?d=0BAJUDYX
Galaxy One Click Root - http://www.megaupload.com/?d=MDKSSSX5
Heimdall - http://github.com/downloads/Benjamin-Dobel...1.1.1-win32.zip
CM7 Nightly - http://download.cyanogenmod.com/?type=nigh...ce=captivatemtd
Google apps - http://cmw.22aaf3.com/gapps/gapps-gb-20110613-signed.zip
MS C++ redist - http://www.microsoft.com/downloads/en/deta...23-37BF0912DB84
Samsung USB Driver - http://www.megaupload.com/?d=9CE6UFMP
ClockworkMod Recovery - http://www.megaupload.com/?d=0BAJUDYX
Galaxy One Click Root - http://www.megaupload.com/?d=MDKSSSX5
Heimdall - http://github.com/downloads/Benjamin-Dobel...1.1.1-win32.zip
CM7 Nightly - http://download.cyanogenmod.com/?type=nigh...ce=captivatemtd
Google apps - http://cmw.22aaf3.com/gapps/gapps-gb-20110613-signed.zip
MS C++ redist - http://www.microsoft.com/downloads/en/deta...23-37BF0912DB84
Samsung USB Driver - http://www.megaupload.com/?d=9CE6UFMP
Once everything has been downloaded, make sure to install the USB drivers first. Your phone should be recognized by your PC and this has all necessary drivers to facilitate this process. Your phone will be in different modes and different drivers are needed for each mode. Make sure this has been installed and your phone is seen by the PC. I assume you have good file management skills, if not put this all into a simple folder, I called mine "cyanogen" and placed all files inside this folder.
Starting the modding process
Install Clockwork Recovery MOD
So now your phone is ready to be modded
Boot your phone into "Download Mode". Plug your USB cable into the PC, but NOT into the phone just yet. Hold down the volume buttons (both + and -) then plug the microUSB end in the phone, keep holding the buttons until you get into this screen.
Navigate to "heimdall\drivers" and run the program zadiag.exe. Choose "Options" and click on "List all devices". The box in the center screen will populate with a list of devices. Drop that center box down to "Samsung USB Composite Device" and click the button for "Install Driver". This can take a few minutes to complete, be patient. Once complete this window can be closed.
Go back to the "hemidall" folder and launch "heimdall-frontend.exe". You will see 10 boxes with Browse buttons next to them. Select the Browse button under Kernal (zImage). Navigate to ClockworkMod Recovery\zImage-Captivate. Click Start, if it fails, just try it again, it will work. I clicked it too fast one time and it failed on me, the second time it worked fine. Congrats, you got a modded recovery menu.
Obtaining Root Access
Galaxy One Click Root process
At this point I obtain root access to the phone. Rooting the phone allows full access to it allowing you to complete any actions your apps need. This process is very simple, hence the name Galaxy One Click Root, its literally one mouse click. Open the program under "Galaxy One Click Root\Galaxy_One-Click_Root.exe". Make sure your phone is connected to your PC. Click "One-Click Root". It will reboot into Clockwork Recovery, navigate to " -apply update from sdcard" by pressing the volume - button and press power to select it. Once that is done, your phone is rooted. Very simple process.
Installing CM7
The Last Step
While still in recovery (If you are not in recovery, power down the phone and hold the volume buttons (+ and -) and press power to get back into recovery), go down to the option "-mounts and storage", select it with the power button. Choose "-mount USB storage" near the bottom of the list and copy your Cyanogen Mod 7 zip file and the Google Apps zip file to the root of the SD card. Choose Go Back to return to the main screen of the recovery menu.
Select the option to Wipe data/factory reset. Then select the option to Wipe cache partition.
Choose "-install zip from sdcard", then "-choose zip from sdcard". Select the zip file for Cyanogen Mod 7. Let it finish and it should reboot into CM7, congrats its modded.
If you want your Google apps, boot back into recovery and install zip containing the Google apps.
Welcome to CM7
I don't know who made all these apps, but all credit goes towards their authors. If there are any issues with any links provided here, let me know, I will modify/remove whatever is necessary.