I also have a Dell laptop, and had the same problem, I can tell you that the problem is almost certainly that you are brushing the touchpad with your hand while typing, mine responds to even the slightest touch.
There should be a setting in the touchpad properties in Control Panel called "Palm Check" or something similar that will attempt to detect when your palm is brushing the touchpad, but I found that it really never helped me. You can also decrease the sensitivity of the touchpad, but then it becomes that much harder to use it the rest of the time.
Another solution would be to get a USB mouse, and then in Control Panel you set it to disable to touchpad when a USB pointing device is connected. That's what worked for me.
Hope that helps.