Step 1: Download iOS 4.3.1 for your device (download links at the end)
Step 2: Update/Restore to iOS 4.3.1 firmware using the IPSW file via iTunes 10.2.1.
Step 3: Start Redsn0w and point it to the official iOS 4.3.1 firmware file.
Step 4: Now simply select “Install Cydia” and click “Next”.
Step 5: Now make sure your device is both OFF and PLUGGED IN to the computer before you click “Next”.
At this stage you will be presented with a screen where you will be guided on how to enter DFU mode. Quickly hold “Power” button and then while holding the “Power” button, you will now have to hold “Home” button too. Now after few seconds release “Power” button but keep holding “Home” button until installation begins.
Step 6: Wait shortly. Once done, your iPhone, iPad or iPod touch will restart automatically and you will find it fully jailbroken (untethered) on the latest iOS 4.3.1 firmware.
Download Redsn0w 0.9.6rc9 (Windows)
Download Redsn0w 0.9.6rc9 (Mac)
Download iOS 4.3.1 for iPhone, iPad and iPod touch
Download iTunes 10.2.1 for Windows / Mac OS X