As of October 2015, websites for Good Knit Kisses, Loom Knit and Lion Brand Yarns have free instructional videos on loom knitting. Good Knit Kisses offers numerous videos and organizes them by category, such as cast-on, bind-off, stitches, patterns and techniques.
Good Knit Kisses also has links to other videos it has reviewed. Loom Kit's video page opens with several basic topics, such as different types of stitches. More complicated subjects include making socks, increasing stitches, picking up dropped stitches and knitting dishcloths.
Lion Brand Yarns' site has a few videos geared specifically for the Martha Stewart Crafts Knit & Weave Loom Kit. They provide introductory information, including how to use the pegs and create different designs.