My Grandmother actually taught me how to crochet a granny square. And from what I've seen in patterns you can start out many different ways. But this is how I like starting out:
Round 1
Ch 3, 2 dc in 3rd ch from hook, ch 1, (3 dc in same spot as last dc, ch 1) continue 2 more times, connect round with sl st to ch 3 spot. Break off, weave in ends
Round 2
Connect at any ch 1 spot, ch 3, 2 dc in same spot, ch 1, 3 dc in same spot, ch 1, (3 dc in next ch 1 spot, ch 1, 3 dc in same spot, ch 1) continue ( ) all the way around, connect round with sl st to ch 3 spot, break off and weave in ends.
Round 3
Starting in the corner of a ch 1 spot, connect thread, ch 3, 2 dc in same spot, ch 1, 3 dc in same spot, ch 1, 3 dc in next ch 1 spot, ch 1, 3 dc in next ch 1 spot, ch 1, 3 dc in same spot as previous 3 dc
Continue this process for as many rounds as you would like.
Remembering that in every corner spot you should have 3 dc, 1 ch, 3 dc
and that along every edge in each ch 1 spot you should have 3 dc, ch 1, and then move on to the next ch 1 spot.
For a fancier look try fancier stitches such as the puff stitch.
