I always have used a yarn needle with the same yarn as used in your Granny squares - double the yarn for extra strength. Then just use the whip stitch, over and over, threading your needle beneath the "horse's hoof" top of each stitch on the two squares you're joining. Since all the squares were done from the same pattern, you should have the same number of stitches on each side of the two squares you're sewing together.
Crocheting them together is another option - this creates a smooth right-side and a ridged wrong-side to your piece. But it is a bit stronger than the sewing technique.
Hope this helps,
My words sell the Magic of a Dream