This is one of the most common questions on intarsia. The method I copied is basically saying to drop the background color, knit the first stitch with the new color, but before knitting the second stitch with the new color, drop it, hold the old color over to the left, over the yarn that's hanging from the new color. This way the new color comes up from under the old color.
It is confusing. Here is a site dedicated to intarsia. I believe they say to tie a square knot, if I'm not mistaken.