To make this scarf you will need to use a single crochet stitch and a chain stitch. Also I am using a size 'K' or 6.5mm hook, but you can use whatever hook size you want.
You'll want to start off by making a slipknot. If you don't know how to make one this picture below shows you how.
Put the loop on your hook and adjust the size of the loop as needed. To make the chain stitch, all you need to do is wrap the string around the hook like shown below, and pull it through the loop.
You have just had made one chain stitch or 'loop'. To begin the scarf, you will need to make about 224 of these. Of course that seems like a lot, but that's because this is going to be the length of your scarf. I personally like my scarfs this length, but you can choose to make your scarf longer or shorter. Once you're finished with that, to start the first row of your scarf you need to make a Single Crochet Stitch like shown below.
To start off you want to put your hook through the second loop rather than the first. Below I have a poorly drawn circle over the loop you want to put the hook through.
Then you want to wrap the loop around your hook and pull it through the place where you put the hook through. You should now have two loops on your hook. Then wrap the yarn around the end of the hook and pull it through the two loops so that you now only have one loop on your hook. And there you go!
Keep making these stitches all along the row of chains to complete your first row. Keep making rows like this until your scarf is the thickness that you want it to be. And that's all there is too it! For a really in depth, slow, step by step tutorial, check out the video below. This is the video I watched to learn how to make a single crochet stitch and it's extreamly helpful for beginners!