According to the National Watermelon Promotion Board, you should look for the spot at the bottom of the watermelon where it had sat on the ground. When the watermelon is ripe, that spot should have has a creamy yellow color.  If that spot has some green in it, the melon is probably not quite ripe yet. A yellow spot means the watermelon was ripen on the vine before it was picked.  That gives you the best flavor. When you lift up the melon, the weight of the melon should be heavy. Over 90% percent of it is water.
When the weather is hot, a watermelon will ripe in a little more than a month after the flower blooms. 
Here is a helpful video for more information: