Reddit mentions of Getting Started Knitting Socks (Getting Started series)

I learned how to knit socks using Getting Started Knitting Socks by Ann Budd. If you can find a copy at a library, I highly recommend checking it out.

Ann Budd very thoroughly covers sock anatomy and common problems with sock knitting (though, admittedly, top-down only). The book also contains basic sock recipes for multiple sizes (from small kids socks to large men's socks) and gauges (from 8 stitches per inch/fingering to 4 stitches per inch/bulky). Finally, it has guidelines to convert shoe size to sock length/circumference.

Overall, I think it's a great resource, and I find myself returning to it to adapt other sock patterns to different sizes or gauges.

Otherwise, if you're set on free, online resources, Silver's Sock Class and Tin Can Knit's Rye are also great, as others in this thread have mentioned.

I would get get two 32-inch circular needles in the same small size, probably US 1's. That way she can have two socks going with magic loop method, or she can try out socks on two circulars (which is my preferred method, so I often mention it).

A couple skeins of fingering. I suggest getting a midpriced yarn for a first effort, such as Opal 4-fach, Reggia, or Zitron Trekking, and perhaps a deluxe sock yarn such as Lorna's Laces Shepherd Sock. These yarns are found in yarn specialty stores (Local Yarn Store or LYS), not big box stores.

There are a lot more yarn choices available online, but you're out of time.

Perhaps the wisest thing to do would be to get her a gift certificate to KnitPicks and then sit down with her one day to make up an order. They sell good workhorse yarns and good mid-range needles and notions.

For instructions, consider Ann Budd's Beginner Sock Book but honestly, I think Lifestyle Toe-up Socks and Silver's Sock Class, both free online, are fine for learning.

The heel flap is worked flat, usually with a slipped stitch texture and over half your stitches. The other half will just hang out until you're done with the heel flap and turning the heel. When you turn the heel, you work short rows which give a little pocket for your heel. Then you will pick up and knit up one side of the heel flap, across the instep (top), and then down the other side of the heel flap. The beginning of your row will now be in the center of your heel and you will begin decreasing out the extra stitches on either side of your instep, creating the gusset.

I highly recommend you get a good sock knitting reference like Getting Started Knitting Socks. The pictures and explanations will help a lot.