There are videos here on KH on the Tips page
that can help you with joining the yarns. I would probably choose the "knit in join" method beginning the method at a point where the next 3 sts are in the color that you're joining. To simplify things and reduce bulkiness, I would also not
join both at the same time; in other words, join your first color to the new ball of same color working it over 3 knit stitches then join your next ball of that second color and work it over 3 sts.