Launch the Mac App Store from your dock.
Click to select OS X Mountain Lion from the list of applications on the right.
Click the $19.99 button under the Mountain Lion icon then click the green Buy App button that appears.
You will be asked to log into your iTunes account. Enter your login information and click the Sign In button.
Launchpad will open and your OS X Mountain Lion download will begin. Press Escape to close Launchpad.
You can view the progress of your download by switching to the Purchases tab.
Once the download has completed the OS X Mountain Lion install wizard will open. Click the Continue button to begin.
Click Agree to accept the software license agreement.
Make sure the correct hard drive is selected for installation and click the Install button.
You will be asked to enter your administrative name and password. Enter these and click the OK button.
OS X Mountain Lion will prepare the installation. Your computer will restart automatically.
Once your computer restarts the installation will begin. This process can take from 15 minutes to an hour.
When the installation has completed successfully your computer will again reboot.
Once the system has finished restarting you are ready to begin using OS X Mountain Lion.