You actually do /not/ TinyUmbrella to run its TSS Server or point to Saurik's SHSH caching server--the iPhone 3G does /not/ use SHSH blobs at iOS 3.1.3. However, I'd recommend using TinyUmbrella to bypass the error you'll get at the end of your restore(s).
0) Make sure you have all necessary files--TinyUmbrella, iTunes, and a 3.1.3 IPSW for the iPhone 3G (iPhone1,2).
1) Plug your 4.2.1 iPhone into your computer. Then place it in DFU mode (hold the power + home buttons on the phone for ten seconds, then let go of the power button and continue holding home for ten more seconds). When iTunes tells you an iPhone has been detected in "recovery mode" but the phone's screen is black (like it's turned off), proceed.
2) Hold down Shift (Windows) or Option (OS X) and click "Restore" in iTunes. Navigate to the 3.1.3 IPSW you downloaded.
3) Let the restore run its course. It should end with an error. Any error with a 10xx code is normal and expected.
4) After the restore errors out, open TinyUmbrella and hit the "Exit Recovery" button with your iPhone selected.
TIP: If your iPhone does not exit Recovery mode after hitting "Exit Recovery," repeat the Shift or Option + Restore to 3.1.3 again. DFU mode is not needed, you can restore immediately from the "connect to iTunes" logo.
5) If your phone is now on the "Emergency Call Only" screen, plug in your legitimate SIM card to activate with iTunes. You can also use a jailbreak tool to hacktivate your phone if you don't have a SIM.
6) Jailbreak with the tool of your choice, if you so desire (available tools are Spirit, jailbreakme.com, and redsn0w 0.9.4. Please note the only tool capable of hacktivating 3.1.3 is redsn0w).