ODIN/Download Mode
Make sure your device is completely off
Key Combos: Volume Down + Home
While holding both of them simultaneously press the Power button until you see a disclaimer on the screen
Then let go of all the buttons and press Volume Up to accept the disclaimer
Once the green robot is visible on the screen this indicates that handset is in now ODIN/Download mode

Recovery Mode
Make sure your device is completely off
Key Combos: Volume Up + Home
While holding both of them simultaneously press the Power button
As soon as the phone vibrates, let go of the Power button but keep holding Volume Up + Home
When you see the "Samsung Galaxy S III" logo (not just the word "Samsung"), right after that, the next screen you should see is your recovery