Ordinarily, stitches are knitted in the same order in every row, and the wales of the fabric run parallel and vertically along the fabric. Welcome to the wonderful world of knitting! Even if you've been here for a while, there is always something new about this most fascinating craft!
It is very easy to knit a sock, in the sock-knitting machine. You could even teach a "keep up" class where people who have completed all three classes meet once a month or bimonthly to keep in touch with knitting. But to develop this fabric you will need some devices with which you will be able to knit with.
Some yarns are dyed to be either variegated (changing color every few stitches in a random fashion) or self-striping (changing every few rows). The earliest examples of this technique are thought to have been knitted around 1850. Take it from me, when you knit-it-yourself, it feels good!
Good luck with your knitting. You may also want to consider finding a local knitting group or meeting online others who share your hobby.