When I come to where I need to add in another ball of yarn, I do the stitch until the final pull through then do the final YO with the new ball of yarn and do the final pull through.
I.e. for a single crochet: Insert hook into the stitch, yarn over, pull through the stitch, do YO w/new ball of yarn and final pull through.
At the final pull through you drop the old yarn and use the new one. I hope this makes sense.