If you want to flash a custom ROM to a Galaxy S III then you can do so by flashing a zip file in Recovery as you would on any other device. If you want to flash a stock ROM you can do it using Mobile Odin.
Download the app
You can download Mobile Odin from here: http://bit.ly/XNX5IL. The app enables you to flash stock Samsung ROMs without increasing the flash counter, meaning you can update – or roll back – your device without affecting any future warranty claims you might have.
The app requires root to run, so grant this when prompted. You can use Mobile Odin to flash a new kernel to your phone. Simply select the Kernel option when you launch the app and then choose your downloaded kernel from your memory card.
Flash a ROM
ROMs you can flash in Mobile Odin need to be in the .tar or .md5 format. Scroll down and select Open file the choose your downloaded ROM from your internal or external memory card. No other settings need be changed, so scroll down to Flash Firmware, select that and you’re done.