Horizontal stripes are the easiest. Do two rows with one color, then drop it, and do two rows with the other color, repeat.
The easiest way to alternate stripes vertically, is with Fair Isle technique (see video in the Advanced Techniques section). The back will have loops, but it might not look bad.
Remember to avoid doing the scarf in stockinette stitch (Basic Techniques/ More page), because it will curl into a tube.
Hope that helps.
KnittingHelp Queen Bee
"There is a vitality, a life force, an energy, a quickening that is translated through you into action, and because there is only one of you in all of time, this expression is unique. And if you block it, it will never exist through any other medium and it will be lost. The world will not have it. It is not your business to determine how good it is nor how valuable nor how it compares with other expressions. It is your business to keep it yours clearly and directly, to keep the channel open. You do not even have to believe in yourself or your work. You have to keep yourself open and aware to the urges that motivate you. Keep the channel open."
— Martha Graham