This is what I do. Obviously you will be starting at the beginning of a row. I tie the new color onto the old color with a slip knot, loose enough so it can be undone later. Start knitting with the new color. Do this at each color change. You can snip the old color each time, leaving about a 6" tail for weaving in later. When all is said and done, undo the slip knots at the color changes, make sure the two colors are twisted once together (otherwise there will be a hole or gap where the switch was made), then weave each color into its corresponding section of knitting.