Kappy almost got it right.
What he didn't mention is that you need to get your files off and out of Mountain Lion program versions into neutral states as possible so they can be imported into 10.6 compatible versions of programs. Newer propreitary versions of programs alter their files and thus can't always be read by older verisons of software comaptible with 10.6
How to revert your Mac to Snow Leopard
iTunes folder should work in 10.6 as when you update to 10.6.8, it's iTunes 11 just like on 10.8, if not then you can extract the content manually.
iPhoto Library, you really should export all those pictures (right click on iPhoto Library and "show package contents" for the Originals folder), also in any other program that newer versions of software may have altered their support files containing your originals. Like Aperture or Lightroom etc. Their packages also can be right clicked on and opened.
You need files into neutral formats like jpg, gif, txt, mp3 and so forth so they can be imported easily into 10.6 compatible versions of programs.
How to revert your Mac to Snow Leopard
Save everything you can (like exporting bookmarks, passwords, email addresses etc) to a external storage drive, DO NOT use TimeMachine as it doesn't work in reverse. You CAN make a Carbon Copy Clone of the 10.8 boot drive, then access it from 10.6 later, but I wouldn't take a chance on that alone.
Most commonly used backup methods
Once you have you files off, and the drives disconnected. Like in #1 Kappy said, but he didn't mention how to boot off the 10.6 disk, you do this by holding the c or option key down on a wired or built in keyboard.
When your Erasing the ENTIRE INTERNAL DRIVE in Disk Utility (this is a must!), you should take this opportunity to Security Erase > Zero All Data, this will take some time and really check the drive out for errors and map them off, it's worth it for a much more reliable hard drive that has less software issues later on, it acts like a perfect running machine.
If you don't erase the entire drive by selecting the drive makers name and disk size at the top, and only erase the Macintosh HD partition, 10.6 will install, however if you later have a problem you can't repair the drive using the 10.6 install disk because the hidden altered GUID and Recovery HD partitions are on there from 10.8 and 10.6 Disk Utility doesn't know what it is so it can't fix it.
At this point this method will work
How to erase and install Snow Leopard 10.6