I'm about to take matters into my own hands... but where do I begin?
Many of the forum threads out there contain the information needed to install a custom ROM, but the information is scattered about here and there which is confusing and not exactly confidence-inspiring. That's all about to change...
Step 1: Rooting Your Phone
The first step to installing a custom ROM is rooting your phone. This allows you to gain access to protected bits of your phone that you'll need in order to backup your existing data and the ability to install that custom ROM.
The easiest way to do this is to use the One-Click Root application for the Captivate, but before you can do that, first you need to download and install the Microsoft .NET Framework 4.0 and the Samsung USB drivers onto your computer.
Once you install those two pieces of software on your computer, the next step is to download the One-Click Root zip containing the easiest program I could find to root your phone for you.
Now you'll need to configure your Captivate's USB debug settings. To do this, first make sure you are at your phone's Home screen. Then tap the Menu button on the lower left-hand side of your phone and select Settings. Scroll down and tap on the Applications item. You should see a Development option. Select that and then enable the USB debugging checkbox at the top.
Now connect your Captivate phone to your computer via a USB cable.
Unzip the zip file and run the One-Click Root program. This will pop up a window with the Samsung Galaxy S logo and two buttons on the right ("One-Click Root" and "One-Click Unroot"). Click the button that says "One-Click Root".
This will cause your phone to reboot into a mode allowing you to to use your phone's volume buttons to navigate a text-mode screen of menu options up and down. Follow the directions in the blue text-mode window on your computer screen and select the reinstall packages menu item on your phone. Press the Power button to start the process.
After the process is complete, your phone will reboot again - this time it will boot you back into the normal mode that you are familiar with.
At this point, it is safe to disconnect your phone from your computer.
For an extremely helpful video to walk you through the process of rooting your phone, watch this video.
Step 2: Backing Up Your Phone
It is always a good idea to make a backup of your phone before proceeding any further, so here's how to do that:
Open the Android Marketplace application and search for and install "Titanium Backup", the free version is fine.
Once that finishes downloading, run the Titanium Backup program and tap on the Backup/Restore button at the top of the screen.
Select each of the apps you'd like to backup and click the Backup! button for each. Next, tap the Menu button, select More and then Create "update.zip"... and follow the directions on the next screen before finally clicking the button to create the update.zip file.
At this point, you'll want to copy that update.zip file along with the folder named TitaniumBackup off your phone and onto your computer. To do this, first go back to your phone's Home screen and then click Menu. Select Settings, Applications, and then USB settings (if this pops up a menu saying you'll need to disable USB debugging, just click OK). Now select Mass storage and then click Home again.
Re-connect your phone to your computer via the USB cable and then pull down the notification tray from the top of the screen on your phone.
Select the USB connected item which will pop up a dialog box with two buttons: Mount and Unmount. Select Mount. This will allow your computer to view the contents on each of your phone's internal memory drives.
On your phone's main drive, you should find a file named update.zip and a folder named TitaniumBackup. Copy them over to your computer for safe keeping.
Step 3: Install A Custom ROM
Keeping your phone connected to the computer from the previous step, download the ClockWork Recovery zip and then copy it over to your phone, renaming it to update.zip (overwriting Titanium Backup's update.zip if it is still there from Step 2).
Once you've downloaded the zip file containing your chosen custom ROM (I'll be installing the latest version of Cognition), you'll need to copy the downloaded zip over to your phone's internal memory drive.
Once you've done that, disconnect your phone from your computer and turn off your phone. Next, hold down both volume buttons and the power button at the same time. This should boot you into an Android system menu.
Select reinstall packages using the volume-down button to select it and then pressing the power button to activate. This will install ClockWork Recovery and then bring you back to a green text-mode menu screen (if it doesn't, select reboot system now, turn off your phone and try the procedure again).
Select the install zip from sdcard option using your phone's volume buttons and press the power button.
At the next green menu screen, select choose zip from sdcard.
Navigate the file system to select your ROM zip file and then press the power button.
Finally, confirm that you want to install the ROM by selecting the Yes menu option.
At this point, your phone should be installing the custom ROM that you've chosen. This will take a few minutes, so go watch some TV, update your Facebook page, or go tweet about how you're installing your custom ROM on your Captivate phone (make that a few dozen tweets, because installing will take a while).
Note: If the "Installing..." screen stays at "Finding update package..." for more than a minute or two (this always seems to happen to me), something is probably wrong. Simply pop out the battery and then boot the phone into recovery mode and try again.
Once the install is complete, you'll find yourself back at a green menu. Select +++++Go Back+++++. At the next green menu screen, select reboot system now and press the power button.
The first boot up will likely take longer than normal (Cognition's ROM gives you cool female computer voice updates explaining what it is doing), so don't be discouraged if it takes a good 5 minutes or so to boot up.
Congratulations, you've just installed your custom ROM!
Step 4: Restoring Your Applications
The first thing you'll need to do is open up the Android Market application and install Titanium Backup again (or you could connect your phone to your computer and copy the update.zip that was created by Titanium Backup program back onto your phone and reboot it into recovery mode to install the update.zip that way).
If you installed Cognition, like I did, then it will come pre-bundled with Titanium Backup so you'll have everything you need.
Launch Titanium Backup and tap Backup/Restore. Next, press your phone's Menu button and select Batch. This will bring you to a menu of actions with a "Run" button next to each one. Scroll down to Restore missing apps with data and then tap the Run button next to it, following the instructions that follow.
At this point you may need to reboot your phone in order for some of your apps to be seen by the phone (since some may need to be there at boot-up), so go ahead and do that.
You are now finished!