"It says to use Intarsia method, which I assume means carrying the colors across the back as I change them."
I believe you're thinking of stranded colorwork (where you carry the color across the back.) Intarsia is usually worked from bobbins and not carried across the back.
Here's a link that explains it... although someone might have a better place http://sweaterscapes.com/intars.htm
(Edit: Apparently there's a video under advanced techniques too... I haven't watched it, but I'm sure it's as fabulous as all of the other videos)