First you have to ensure the machine is running 4GB or more of RAM. Your machine has the ability to handle 6GB, OWC (www.macsales.com) carries a 6GB kit.
Next is using SuperDuper or Carbon Copy Cloner backup your system onto an external HD. Do this before doing ANYTHING else!!
Next order Snow Leopard's upgrade DVD from Apple, this is only available from Apple's online store. In the US the link is:
Follow the instructions that come with SL to install it, then download and install the 10.6.8 Update Combo to bring SL up-to-date. Then run Software Update and install all the suggested updates.
After you have SL running well then purchase Mountain Lion from the Mac App Store and follow the on-screen directions. Again after it's installed run Software Update to install all suggested updates.
Remember any software that is PPC (PowerPC) based will not run in ML! If you have any old applications it's time to upgrade or replace them prior to beginning the upgrade process. How you can tell is open System Profiler, click Applications on the left pane and then look in the Kind column, anything marked PPC will not run in ML.