These are instructions on how to
If you want to a lower firmware version you can find the appropriate tutorial here.
Make sure not to update to .1 if you need an as one is not yet available!
Create a folder on your desktop called Pwnage
Download from here and place it in the Pwnage folder. Likewise, download the latest 4.3.1 firmware from below and place it in the same folder.
4.3.1 (4 GSM): iPhone3,1_4.3.1_8G4_Restore.ipsw
Extract the RedSn0w zip file by double clicking it.
Connect your to the computer and launch iTunes.
Select your iPhone from the list of devices on the left. Now hold down Option and click the Restore button. Restore is preferred as it won’t create any wasted space on your iPhone.
Navigate to the Pwnage folder on your desktop and select the 4.3.1 firmware ipsw. Click the Choose button to continue.
Once iTunes has finished updating your iPhone to the desired firmware open the Pwnage folder on your desktop and launch the redsn0w application from the redsn0w folder we extracted earlier.
Once RedSn0w opens click the Browse button
Select the 4.3.1 firmware ipsw we placed in the Pwnage folder on our desktop then click Open.
Once the firmware has been verified click the Next button to continue.
RedSn0w will now prepare the jailbreak data
From this window you can select the jailbreak options you would like.
Please plug your iPhone into the computer and make sure its OFF then click the Next button
RedSn0w will now guide you through the steps to get into DFU mode. You can find more help with DFU mode here.
Hold down both the Home button and the Power button for 10 seconds.
Release the Power button and continue holding the Home button until RedSn0w detects the device.
Your iPhone will now reboot
RedSn0w will then begin uploading the new RAM Disk and Kernel.
Once this is complete you will be notified that RedSn0w is done. Click the Finish button. When your iPhone finishes rebooting (5 minutes or so) it will be jailbroken with Cydia on the SpringBoard.
*As usual a big thanks to the iPhone Dev-Team and I0n1c for their hard work and contribution to the iPhone community.