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.