This is your basic Tunisian stitch, aka afghan stitch, simple, knit and tricot stitch. Once you master this one, you should be able to do all the variations. More about these later.
First you need an afghan hook. I suggest you go with a larger size for your first lesson.
You start with a chain just like any other crochet you've done. Chain about 20 for this. Then you take your afghan hook and insert it into the second ch from the hook, yarn over (yo) and pull it through. You should have two loops on your hook now. Leaving this loop on the hook, proceed to do the same in the next ch and all the way to the end. DO NOT TURN.
Yarn over(yo) and pull through the first loop on the hook. YO and draw through the next TWO loops on the hook. You are now working from left to right. Continue to YO and draw through the next two loops on hook. The stitches are coming off the hook as you work them. At the end of row one you should have one loop left on your hook.
Watch your tension. You need to be as relaxed as you can be. Keep the tension loose enough on the yarn that you are not fighting it. If the yarn is too tightly stitched the project will tend to roll. Relax. You can do this. Go with a bigger hook if you have to.