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I had this ball of mohair lying around, no tag, hot raspberry pink. No idea what I bought it for, but I do like pink. It ended up being this fuzzy shrug, perfect as a little layer over a tank top. Mary loves it.
To make a shrug of your own, all you need is a rectangle. If your shrug recipient is nearby, you can measure from shoulder to shoulder, add a little bit for the "sleeves" and then measure from the top, where it would hit the neck, down as far as you want it to go. Knit a rectangle to these dimensions, and then seam a little on the front to create the sleeve part. You can add the yarn-overs or not, or add some other interesting stitch or not - with a hairy enough yarn it doesn't matter anyway, but if you're using something that shows stitch definition you can put them in.
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For this shrug, which would fit a child 8 - 10, finished measurements 9 x 20", you need:
One ball of hairy yarn in the color of choice that will give you a gauge of about 9 sts over 4" of garter stitch (the exact gauge is not that critical - this would be fine at 2.5 sts/inch instead of 2.25/inch) on size 10 needles, or the size that'll get you there.
CO 20 sts, leaving a nice length of tail for sewing later
Rows 1 - 5: knit
Row 6 (WS): k1, *k2tog, yo, repeat from * to last stitch, ending with a k1
Rows 7 - 9: knit
Row 10: repeat row 6
Knit until piece measures about 14", ending with a RS row
Repeat Rows 6 - 10
Knit 5 rows
Bind off, again leaving a nice length of tail
Now you have a rectangle. Fold it in half lengthwise and, using the tail ends you left at CO & BO, whipstitch the last 2" or so and weave in the ends. Voila - it is a shrug.
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