If this feels a little over whelming, you may want to start here. This is an instructable I made for complete newbies to crocheting.
Step 1: Making the First Round - From Slipknot to Joining
Make a slipknot with your yarn and insert the hook into the knot.
Chain 4 stitches.
Insert your hook into the first stitch (closest to the slipknot).
Yarn over and pull the yarn through the stitch. Slip the stitch through the loop on your hook.
This creates the ring (center of the granny square), take note of the hole in the center of the ring, this is where all the work will be done for the first round.
Chain 3 stitches.
Double crochet into the ring
Double crochet into the ring again.
This set of stitches is the first "shell" of the granny square. a shell consists of three double crochets together in the same space. Please note that the chain 3 takes the place of a double crochet.
The first round will consist of four shells. You will need to chain 2 stitches between each shell in the first round.
Chain 2 and make another shell by doing three double crochets into the ring. (This is shell number 2).
Chain 2 again, make another shell by doing three double crochets into the ring. (This is shell number 3).
Chain 2, yet again, and make the last shell for round one.
You know how have 4 shells and are ready to join them together.
Chain 2 stitches then insert your hook into the second stitch of the first shell you made. (The second stitch on the chain 3 we did directly after making the ring).
With your hook through the stitch, yarn over and pull through. slip stitch through the loop on your hook.
That concludes the first round. All subsequent rounds are just a repeat of this round. The only difference is the number of shells you will make and the amount of chain stitches between shells.