The little ovals along the bottom are chain stitches, as we can see from the key. The way that they go up the side of the first row of the work shows that the last few chains worked will count as a turning chain or stitch. We see then two double crochets worked into the same chain, several chains that are not worked into, then a single crochet, chain 3, skip a chain, and another single crochet. Then we see 2 double crochet, chain 2, 2 double crochet all worked into the same chain, and then those stitches repeated across the chain. We then see our turning chain (shown in blue to differentiate the rows), a single crochet, and the same stitch pattern as the previous row, worked into the chain spaces created in Row 1.
Working with a written pattern alongside a stitch diagram is a good way to practice reading the diagrams intuitively. Before long, you'll be able to read a pattern directly from its diagram, using the pattern only when clarification is needed, and you may even find yourself drawing your own stitch diagrams for instructions that don't have them! Here's a picture of what the above diagram looks like when it is crocheted (and just wait until you see the whole garment in the book!): |