Here are the basic stitches of crochet and their abbreviations:
|Top to Bottom: Single, Half Double, Double, Triple|
(sc) Single Crochet
(hdc) Half-Double Crochet
(dc) Double Crochet
(tr)Triple Crochet (or Treble Crochet)
(sl st) Slip Stitch
I am one who learns best by watching others. Good thing there is a video accompaniment! Unfortunately, this video has neglected to instruct on how to accomplish a half-double crochet. It is really pretty easy, but it's not a stitch that I use very often (in case you couldn't tell, I am the instructor in this video.) Begin like a double crochet: yarn over, insert hook, yarn over, draw through. You should now have three loops on your hook, yarn over and draw through all three loops. Done. Half-double crochet.
Once you know the basic stitches, you can complete simple projects and combine the basic stitches to make more complex ones. One day maybe I'll instruct on the more complex stuff, but this will get you going for now!