Get an 8GB or larger flash drive or external USB drive, ensure there is nothing valuable on it, and that it has been formatted with the Mac OS file system. You will also need to have the computer connected to the Internet.
If you haven't already accepted the iLife apps into your iTunes account, do this first, otherwise you won't have them available for installation after you install the OS on your new drive. Google will help you figure out how to do this.
With your old hard drive in the laptop, boot into the recovery partition by holding the ALT key down, then selecting the recovery partition option.
When you have booted into the recovery environment, select the appropriate language.
At this point you should have an option to reinstall Mac OS, choose it, and when asked where to install it to, choose the external drive.
The process will download the Mountain Lion installer to the external drive - it is usually the version of the OS that shipped with your computer.
It will reboot when it is done, this is the point you need to remove the external drive from your Mac.
From there you can follow the any guides online that walk you through creating a Mac OS installer USB stick.