What is the correct way to join a new skein of yarn to a project?

If you have finished off the old color, place a slip knot on your hook, insert hook where you want to join the new yarn, yarn over and pull through both the stitch and the loop on hook (making a slip stitch). Chain up however many you need for the stitch you will be making next and continue working with the new yarn.

If you have not finished off, but are just continuing from your present point, work your last stitch before the change in color or skein to the last step, then just lay the new yarn over the hook and complete the stitch with the new yarn.