While knitting is about rows, crochet is about chains. (Well, crochet is about rows too, but you'll hear "chain" a lot.) Chains can be arranged in rows, or clumps, or circles. Making a chain is the base technique for most crochet.
You often need to start with something called a Foundation Chain. Just as the name implies, this is a chain of linked crochet stitches that you will use as a starting place for a piece of crocheted fabric. A foundation chain is also useful in knitting if you are working a provisional cast on.
Start with a slip knot. This is the first stitch in your chain:
With the yarn at the back of the hook, rotate the hook up and away from you, catch the yarn, and rotate it back down. This rotate-catch-rotate is the basic crochet move. The yarn should be going up the back of the hook and then down over the front:
Hold on to the yarn tail to keep the slip knot on the hook open, and carefully pull the yarn through the slip knot. Pull the ball end yarn to tighten the new stitch slightly. Make sure to keep each stitch a little relaxed; you will need to fit the crochet hook through them later:
Repeat the motion, catching the yarn and pulling it through the loop on the hook each time. This is your foundation chain. Each chain stitch looks like a "v" shape from the front, with a bump at the back: