Notice that each chain has three parts--the chain on top has a thread nearest you and a thread farthest from you, and there lies the little bump underneath. For now, let's work into the top single thread of the chain.
That shows how to work single crochet into chain stitch. To work single crochet into another single crochet below, insert the hook into both sides of the chain that lies at the top of the single crochet stitch. That is, for now. Other more decorative stitches are made by working into either the front of the chain or the back of the chain. To practice, just work into the entire chain.
I must mention, by the way, that this lovely blue yarn in all the pics is Malabrigo Worsted in Blue Surf and the hook is Brittany bamboo.