Here is a link to a really simple shawl pattern. It only uses a knit stitch and you will need to learn to k1f&b which is the most common increase you could learn and very simple. You can learn this increase from a video on this site. Here is a link to that page. Scroll down to KFB. It is also called a Bar Increase. If you hold your yarn in the right hand as you work, click the blue camera icon. If you hold the yarn in your left hand click the pink camera.
That pattern as given changes the color every few rows, but you could make it all one color and it would be even easier. Choose a big yarn, like a heavy worsted (Vanna's Choice like) or even a bulky yarn. An interesting yarn would make an interesting shawl. Use a big needle. The gal said 15, but 13 would work too, if you used worsted instead of bulky yarn. And you do need it to be a circular needle, maybe a 36" long one would be long enough to hold all your stitches. Gauge isn't real important, just knit on a needle that gives you a fabric you like, it should probably be knit pretty loose so it will have lots of drape. And you can just work it until you have it as big as you want and then bind off all stitches.
Here is a step by step of what you do:
Cast on 2 stitches.
Row 1: Knit into the front of the first stitch, don't slip it off the needle yet, twist the tip of your needle around to behind the LH (left hand) needle and knit into the back of the same stitch, then slide the stitch off the RH (right hand) needle. (K1f&b made) Knit the other stitch. (You now have 3 stitches.)
Row 2: Knit the first stitch, K1f&b, knit the last stitch. (You now have 4 stitches.)
Row 3: Knit 1 stitch, K1f&b, knit the rest of the stitches in the row. (Each row you will gain 1 stitch.)
Then over the rest of the shawl repeat what you did in Row 3. Work until it is as big as you want and then bind off all the stitches.