Okay, so when designing for Black T-shirts, the design is opaque right? Which is why they suggest you use a transparent background of course. But is there anyway to use that same technique for the colored shirts at cafepress? Like the pink or green ones for example? When I upload my image and try to add it to these colors, the design color is distorted because the color from the t-shirt is showing threw the design. Does anyone know what I mean? And if so, is there a way to work around that?

That's just the way the printing process is. The process they use for dark is much more expensive and time consuming. That's just the way it is. There really is no way around it.

http://tutortanith.com/designtips3.htm

My guess is that if you use colors that are not fully saturated but need some white to make it, like pink, then that area won't get filled up 100% with color ink and the shirt color shows through.
Deep red = lots of print ink, pink = just a little ink is used.