Hi! I'm working on my first intarsia project too. I found a great way to join a new yarn in the 'Vogue Knitting' book. It actually has 3 options for how to join, but this seemed the least complicated and it actually works really well. Here are the instructions exactly:
"Wrap first the old and then the new yarn knitwise and work the first stitch with both yarns. Drop the old yarn. Work the next two stitches with both ends of new yarn. Drop the short end of the new color and continue working with the single strand. On the following row, work the three double stitches as single stitches."
It sounds a bit odd, especially the part about using BOTH colors together for the first stitch, like you're going to end up with some multicolored stitch there, but you don't AND it weaves in the end at the same time.