Note-this will void your warranty. Secondly, there are a few minor bugs that you should know of: FM radio does not work, using the flash in Camera app may cause it to crash and trying to wake up the device using volume keys “may” not work, so there you have it.
Step 1: Root your Galaxy S III and flash ClockworkMod Recovery to it.
Step 2: Download the latest nightly build of CM9 [CM Downloads] and Google Apps for CM9 [Goo.im]. Transfer both to directly under /sdcard on your Galaxy S III.
Step 3: Shut down your device. Boot into ClockworkMod Recovery by holding the Volume Up + Home + Power buttons.
Step 4: Take a nandroid backup. This will come handy later on if you wish to revert back to previous setup.
Step 5: Navigate to install zip from sdcard > choose zip from sdcard > [CM9 .zip file you downloaded in Step 2].
Step 6: Similarly, you must flash Google Apps.
Step 7: From ClockworkMod’s main menu, perform wipe data / factory reset.
Step 8: Choose reboot system now from the main menu.