Depending on the sensitivity of the touchpad, you don't actually have to be touching. Yeah. Use Matera's link and disable the touchpad while typing. It's better that way.
You can also disablle the tap-to-click on the touchpad, which may help with part of the problem. The cursor moving is harmless, but once it's 'clicked,' that's when you'll start typing somewhere else.
You may also want to look at how you hold your wrists. Resting them on laptop below the keyboard is very, very bad form ergonomically.
I turned off the scrolling, the tap-to-click, and turned down the sensitivity on my trackpad. Now it functions ONLY to move the mouse. And I am happy. (I do really like my lappy... and am sad that it's starting to see intermittent hardware failure. =(