Pick Up a Dropped Stitch
When I have to pick up a dropped purl stitch, I always turn my work to the wrong side so I can pick it up as a knit instead. I only use my needles for this (no crochet hook or extra tools needed), which I find more convenient. You can, of course, use this method for a knit stitch too - just don't turn your work to the WS before beginning.
Notice that I purl the picked-up stitch through the back loop after fixing it since my method turns it around from the usual orientation (leading leg of the stitch is in back rather than in the front.)