Start with your slip knot loop around your hook as before.
Wrap the yarn from left to right around the back of the hook.
Pull the yarn strand down through the loop that is already on the hook.
Now the strand has become the loop around the hook. You have just created one chain stitch.
Continue your chain by wrapping the working yarn strand around the back of the hook from left to right as before.
Pull the yarn down through the loop on the hook.
There you have it, another chain stitch! Now you have two. See the two "V's" to the left of the hook? Those are your chain stitches.
Continue your chain until you have the number of chain stitches called for by your pattern, or until the chain is the width you want it to be for a beginner's scarf or potholder.
Have questions? Always feel free to ask them in the comments :)