Is this just a simple work back and forth on straight needles type of scarf? If so, and I understand this is just a striped scarf, all I do to start a new color is to start knitting with it. Some people do things like tie the yarns together, etc. but I just take the new color, on a right side row and begin knitting with it. You can cut the first color leaving a good tail to work in. The first stitch or two will seem loose, but when you pull on tails they tighten up and I just wait until I'm done and pull the edge stitches into position and then work the tails into their own colors.