How to jailbreak your iPhone 1.1.3 firmware

So after all the rumours and waiting the iPhone Dev Team finally release the jailbreak for the iPhone 1.1.3 firmware
This jailbreak comes with a forewarning on how difficult this upgrade is compared to the others so be sure to backup as you may need to restore your iPhone using iTunes if you run into any problems.

This latest jailbreak also comes as an upgrade so you must already have a 1.1.1 or 1.1.2 jailbroken phone before attempting this.

1.1.3 soft upgrade jailbreak.

MAC VERSION - Download the 1.1.3 package maker and execute Run_This. Read instructions, pressing Enter when prompted, and the image will be uploaded to your phone. Then continue to the Installer instructions below.

• You must begin with a 1.1.1 or 1.1.2 jailbroken phone with Installer.app installed and AT LEAST 300mb free space on your iPhone and 1GB spare on your computer.
• Connect your phone via USB to your computer.
• Download, extract, and run iBrickr Special 1.1.3 jailbreak edition (ibrickr.exe is in the archive).
• iBrickr will determine what firmware you are running on your phone and confirm you can apply the update..
• iBrickr will then guide you through the process of obtaining and modifying the 1.1.3 firmware
• iBrickr will upload the new firmware image to your phone. Please note that this only uploads the file on your phone and does not modify it at all.
• When iBrickr finishes (should take about 10 minutes), it will tell you to go to Installer and install the “1.1.3 soft upgrade” package. Do that.
• The upgrade will pause about halfway through the process. THIS IS NORMAL. DO NOT INTERACT WITH YOUR PHONE WHILE THIS IS HAPPENING. Just leave it plugged in and wait
• When the installer has finished (this should take another 10-15 minutes), your phone should reboot with a freshly activated 1.1.3 firmware.

and how does this 1.1.3 jailbreak work?

• iBrickr grabs the 1.1.3 iPhone firmware image and extracts, decrypts, and decompresses the disk image.
• Patch is then applied, jailbreaking the disk image and activating it, and also installing Installer.app.
• New modified image is uploaded to the phone, as 113_upgrade_image.bin.
• The “1.1.3 soft upgrade” app flashes the phone with the image and reboots.
• Your iPhone is now upgraded with the latest 1.1.3 firmware, with all your settings and music restored.

this upgrade is by no means safe and more than previous jailbreaks you may run into many problems not least of all a non working iPhone.
Check the FAQ for an idea of what to expect and answers to questions regarding problems running the 1.1.3 soft upgrade from installer, problems after last reboot and PANIC: Everything is broken and I need my phone please help!
Also check this walkthrough of the upgrade process from lifehacker