First, make sure your Mac meets Snow Leopard's requirements Mac OS X v10.6 Snow Leopard - Technical Specifications
You can purchase v10.6 Snow Leopard > Mac OS X 10.6 Snow Leopard - Apple Store
As with any upgrade, make sure to backup your important data first.
Once you have that installed, click the Apple menu icon top left in your screen. From the drop down menu click Software Update. That way you'll have v10.6.8 installed.