This guide describes how to upgrade from 1.1.1 to 1.1.2 including the jailbreak hack.

1. First we're going to restore the device, in order to upgrade the device properly. On my first attempt, I skipped this step, but after upgrading, my springboard woudn't load anymore. Fire up itunes, and click restore. If it doesn't restore to 1.1.1 (i.e.: it restores to 1.1.2) download here 1.1.1, hold alt when clicking on restore, and select the downloaded 1.1.1. firmware file.
2. Next step is jailbreaking the clean 1.1.1 install, just browse to http://jailbreakme.com and click on "install appsnap"
3. Next, open up Installer, browse to the Patches section, and install Oktoprep. This prepares 1.1.1 touches for jailbreaking the 1.1.2 firmware.
4. Now you're ready to install the 1.1.2 firmware. Open iTunes again and click on "upgrade". If the 1.1.2 firmware doesn't show up, download it here, hold alt when clicking "upgrade" and select the downloaded file
5. Let iTunes do its work, when it finishes the upgrade proces, quit iTunes and download 1.1.2-jailbreak.zip
6. Unzip the files in the archive to ~/Desktop/jailbreak, open terminal and type:
   cd ~/Desktop/jailbreak
./osx and let the application do its work.
7. To install the iphone apps, like mail etc, download this archive, and extract Weather.app, MobileMail.app, Stock.app, Maps.app, MobileNotes to /Applications/, GMM.framework to /System/Library/Frameworks/ and MobileMailSettings.bundle to /System/Library/PreferenceBundles/.
8. To extend your Application folder size, read this blogpost.
9. For merging the Music and Video icons, read this blogpost.

are the steps to update your computer to 10.4.10
This is a workable solution for the Asus P5W-DH motherboard, which is running Mac OSx86 10.4.9
/;

0) Before we start..

Copy your extensions folder (System/Library/Extensions) to /Backup/Extensions

Download the latest kernel from #10.4.10 on irc.osx86.hu, or the latest at time of writing Wed May 23 16:33:00 PDT 2007; Sochi2014:VoteForUs/RELEASE_I386 i386 i386

Download R3D3

1) Backup Extensions

We are going to start with the backup proces of a few kernel extensions,
all files will be written to the root of your Mac OS installation partition.
Open terminal and type the following:

sudo -s
cp /mach_kernel /mach_kernel_old
cp -R /system/library/coreservices/loginwindow.app /
cp -R /system/library/extensions/AppleSMBIOS.kext /
cp -R /system/library/extensions/AppleACPIplatform.kext /
cp -R /system/library/extensions/AppleAPIC.kext /
cp -R /system/library/extensions/IOATAFamily.kext /
cp -R /system/library/extensions/system.kext /

2) Running the update

Next thing is running the update in Apple's Software Update
Make sure you keep the terminal and disk utility open

Run Software Update and deselect everything but the 10.4.10 intel update and install it (And do not restart ! Just ignore the installer window!)

3) Restoring Extensions

Right now we need to place the new kernel, the R3D3 kext, and the old kernel extensions to make sure the hardware will work properly after rebooting.

For the kernel (assuming the new kernel is placed on your desktop):

sudo cp -f ~/Desktop/mach_kernel /
sudo chown root:wheel /mach_kernel*
sudo chmod 644 /mach_kernel*

R3D3:

sudo cp -R ~/Desktop/r3d3.kext /System/Library/Extensions/

And the extensions:

cp -R /loginwindow.app /system/library/coreservices/
cp -R /AppleSMBIOS.kext /system/library/extensions/
cp -R /AppleACPIplatform.kext /system/library/extensions/
cp -R /AppleAPIC.kext /system/library/extensions/
cp -R /IOATAFamily.kext /system/library/extensions/
rm -rf /system/library/extensions.*

And on some systems only (first test without, if it fails, boot in single user mode (-s):

cp -R /system.kext /system/library/extensions/
Open disk utility and repair permissions for your OS X partition
Reboot

When things go wrong...

You can always copy Extensions back in single user mode (type -S on the Darwin Bootloader command line ), its really easy, just read the on screen instructions how to mount your drive and get write support enabled.
Copy your old extensions this way:

cp -R /Backup/Extensions/myextension.kext /System/Library/Extensions/

My Ati x1900XT didn't got detected, so I restored my ATi kexts in single user mode:

cp -R /Backup/Extensions/Ati* /System/Library/Extensions/
cp -R /Backup/Extensions/AppleNDRV /System/Library/Extensions/

For nVidia users:

cp -R /Backup/Extensions/NV* /System/Library/Extensions/

(Not tested by me, but confirmed its working, by "Etam" in the comments)

About Audio

My audio didn't work after upgrading, below are the steps which did the job for me:

Move my AppleHDA.kext to your Extensions folder, and fix his permissions.

Reboot

Get the the AppleHDA patcher (v1.16) and my P5W-DH codec dump

Drop the codec dump on the AppleHDA patcher

Reboot