Some of the easiest knitting patterns for beginners are for scarves, washcloths, afghan rugs, blankets and arm warmers. A simple scarf requires a knitter to know only how to cast on, how to make the knit stitch, and how to bind off.
To knit a scarf, cast on as many stitches as required to make the width of the scarf that is preferred. Knit every row until you have reached the desired length of your scarf, then bind off. Once the knit stitch is mastered, move onto the purl stitch, which makes the stockinette stitch when knit, and purl rows are alternated. About.com shows how to use only the knit and purl stitches to create a stockinette stitch washcloth with a seed stitch border that prevents the edges from curling.
The Internet is a source of thousands of knitting patterns for all kinds of projects and many of them are free. Ravelry, for example, is a free online knitting and crochet community that allows members to search for patterns by their level of difficulty, as well as by many other criteria, including user rating, yarn type and needle size. Other online resources include KnittingHelp.com, Knit Picks and Knitting Pattern Central.