A crochet hook can be a huge help, and I don't think size really matters too much as long as it is not way bigger than the size knitting needle you are using.
I've taken to fixing dropped stitches without a crochet hook (although the crochet hook is just a tad faster) because I often don't have a crochet hook handy.
What I do is this:
Make sure you are on the knit side of your work (not the purl side)
Pick up the dropped stitch and make sure it is on the left needle.
Now pick up the yarn that used to be a stitch (you know, the bar of yarn that is created when a stitch has been dropped) and place that on your left needle too.
Now take the right needle and insert it into the dropped stitch and lift it over the bar of yarn that is next to it. Lift it over and off the edge of the needle. Now that bar of yarn has become a stitch again!
I hope my explanation is clear enough!
And I hope it helped!