Try the wrapped technique used in intarsia and fair isle knitting. When you add the new color, loop it around the needle. Before the final step of knitting it off the left needle, wrap the old color yarn around the new strand (both are hanging together." The "wrap" prevent holes. Knots are not the way to go, in my experience. They always end up popping through to the outside. Good luck.
Katie's Mom

I just drop the old color and pick up the new....leaving the ends dangeling. When the sock is finished.....go back and tie the threads together and work the ends into the sock. It's easier to get the tension right and hot to have a tight or a loose place.
Be sure you are tying the knows on the wrong side.
Linda C