Hand-knit socks are warm and fun to wear, but making them is not a task for the beginning knitter. They require small needles and a basic understanding of knitting terms and techniques. You'll probably knit your first pair on double pointed needles. This often results in what knitters call "one sock syndrome" as many knitters find it difficult to actually finish the second sock. If you're one of them, just wear mismatched socks for an interesting look. Later, after you've knit a pair or two with double points, you may want to try the two-at-a-time method using two circular needles.
Find a sock pattern, also available online, and choose a simple one if this is your first attempt. Choose a pattern that starts at the toe of you want to be able to try the sock on as you go to make sure it fits. However, be aware that starting from the toe up is harder than starting at the top. Again, beginning knitters should probably stick with the easiest method. Refer to the pattern for materials. Alternately, many sock yarns come with patterns printed on the labels. Self-striping yarns are fun for beginners because the socks look much fancier than they really are.
Cast on stitches on four needles, spreading the stitches across all four needles. You will be knitting in the round so make sure you don't twist the stitches on the first row. Assuming you are starting at the top, the most common pattern, you will first knit several rounds of ribbing. This helps the sock stay up. Follow the pattern for how many rows of ribbing (or feel free to improvise, it really doesn't matter) and then start knitting the rest of the sock. Pay special attention to the directions for turning the heel. This is one of the trickier parts of sock knitting and there are several ways to do it. Just relax and follow the instructions carefully and you'll get through it. If you are doing the toe last, you will find this a simple matter of decreasing rows.
Once you've made a few pairs of socks, and have the basic idea, you'll find thousands of fun variations!