Craftsy's "How to Crochet Granny Squares" is a good step-by-step guide for crocheting granny squares. The guide covers how to make the center square and how to add more rounds. It also offers tips on putting different colors in a granny square.
The center square includes four clusters of three double crochet (dc). Chain three to start, do two dc into the first chain (ch) to make the first cluster. Chain two to create the first corner. Do three dc into the same chain spot, then chain two. Repeat twice. Finally, do a slip stitch into the top chain of the first "chain three" to close the round and make the center square.
To begin the next round, chain three then make two dc into the same corner. Do three dc, two ch, three dc to make a new corner. Repeat twice to make two more corners. In the final corner, double crochet twice, chain twice and slip stitch to close.
For all the following rounds, start the same way as the second round. Then do three dc if it is a space and a corner pattern (three dc, two ch, three dc) if it is a corner. Keep extend the square until it reaches the desirable size.
To make a multicolor granny square, add a new color after closing a round, or alternate colors within each round. Leave long tails to weave in later.