How to install CyanogenMod 9 stable on Samsung Galaxy S III?
First of all remember that you are the only one responsible if anything goes wrong with your phone.
You will first need to:
1. Root your Galaxy S3
2. Install a Custom Recovery
such as ClockworkMod recovery.
3. Download CyanogenMod 9 stable from here
for Samsung Galaxy S III.
Now you have to follow the next steps:
1. After you download the ROM copy it to your Galaxy S3 SD card.
2. Reboot the device in recovery mode (Hold Volume Up, Home, & the Power button, continue to hold all three until the screen flashes, then release all buttons. ).
3. Use the "backup & restore" option to backup all your data
4. If this is the first CyanogenMod installation apply the "factory reset" option.
5. Now apply "wipe cache"
6. In the "advanced" menu find "wipe dalvik cache" and apply it. Return to main menu.
7. Find the "install zip from SD card" option and click it. You will be prompted with a message to "choose zip from SD card". Choose the zip file containing CyanogenMod 9 for Samsung Galaxy S3 International ROM.
8. Reboot your Galaxy S3
Wait a little before the reboot is finished. You now have CyanogenMod 9 installed on your Samsung Galaxy S III.
You can also watch this video tutorial that shows you how to install CyanogenMod 9 on Samsung Galaxy S III: