Not one pattern but a book of basic patterns for socks of different yarn weights.
Getting Started Knitting Socks by Ann Budd
It includes useful information such as a chart that shows adult men’s, women’s and children’s shoe sizes and foot length and corresponding sections of her book for socks of that size.
I learn better from videos but this was and continues to be a wonderful reference book.
The best book I bought to learn socks is Getting Started Knitting Socks by Ann Budd.
It is ideal for visual learners. Every step to knitting socks is shown. There are patterns for basic socks written for different gauges and yarn weights. I bought it in print back in 2007. After I bought a smart phone I got the Kindle version. It’s handy having the book on my phone for when knitting socks when traveling.
It was an adjustment to dpns, hence knitting them inside out to start (learning curve) but I wouldn’t call it hard. I use wooden dpns and I haven’t had any issues with stitches falling off. I haven’t figured out how to eliminate the ladders after the gusset and decrease.., but for the foot and cuff by switching 2 stitches to the next needle I’ve gotten rid of them. I’ve been knitting top down and needed to watch a few videos to master the heel and gusset along with my book.
Getting Started Knitting Socks (Getting Started series) https://www.amazon.com/dp/1596680296/ref=cm_sw_r_cp_api_glt_fabc_HFPNR11PTMMAKXFRX55Z?_encoding=UTF8&psc=1 And then I picked up the other pattern at my LYS which I love.
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.
Not one pattern but a book of basic patterns for socks of different yarn weights.Knitting Socks by Ann Budd
I used to think I would never be able to knit socks.
Getting Started Knitting Socks Step by step text and pictures guide you through each part of knitting a sock. Sock patterns are written for different weight yarn and knitting gauges. The book has step by step instructions with pictures. If you are a visual learner, this is a great book!
I buy most of my sock yarn from Little Knits. You can usually find really good quality sock wool/nylon yarn for under $10 for 100grams/~400yards.
Wood needles are usually better when starting out. The yarn does not slide off the needles as easily. I like using two or three 16” circular needles. Stitches are divided over two needles. Starting out, it will probably be easier to use three needles.
The first sock is the hardest. It truly gets easier as you practice.
I understand. Most of my knitting consists of shawls. Socks a couple of times a year for my husband. You like what you like!
I suggest Ann Budd’s Getting Started Knitting Socks
or Knitting Socks With Two Circular Needles
Knitting socks on 3 or 4 needles can be cumbersome to learn. I suggest starting off with learning how to knit with double point needles with size 6 or 7 needles with worsted weight yarn at first. Most sock patterns are written for fingering weight yarn with size 0 to 2 needles. It is important to get the gauge called for in the pattern. The helpful thing with Ann Budd’s sock book is that she has a basic sock pattern written for gauges 8 stitches per inch to 5 stitches per inch. I find it easier to knit using 2 16” circular needles (I like Knit Picks or Knit Pro). Your stitches are divided onto 2 needles. You can knit each half with the same needle or knit each half on a third needle, then with the newly empty needle, knit the other half of the stitches. Addi sells sets of three needles for this technique or you can just buy 3 16” needles. I usually use different colors of needles to help me keep track of which half of the socks I am knitting.
Well, I’ve rambled on enough with probably too much information!
My husband likes thick cushy socks. I knit his socks with two strands of fingering weight yarn that averages about 400 yards per 100 gram skein. I use size 4 needles, for a gauge of 5 stitches per inch. Two strands of fingering held together is close to worsted weight yarn. Since I have not found many worsted yarns that are wool/nylon blends like fingering weight sock yarns.
Knit what brings you joy.
Here is a link to a book on amazon. Most of my knitting library has been bought used on amazon. and this is the book that I learned to knit a sock from. I was a new knitter and nothing about a sock pattern made sense to me either. Have I ever knitted a lot of socks in the years since then.
https://www.amazon.com/Getting-Started-Knitting-Socks/dp/1596680296