knock - it should sound hollow.

Look for sugar spots - brown spots and veins. This is the trick my grandpa uses, and he always has the sweetest watermelons!!

The "Melon Meter" app seems to work well according to friends, but I'm not quite capable of whipping out my iPad and thumping melons for it to analyze in public.

The most reliable method requires a refractometer to test the field before harvest although I've seen a less expensive tool called a sledgeomatic demonstrated with very impressive results.

If the spot that was resting on the ground is too pretty and presentable, the watermelon has not been sitting on the dirt too long and thus is not very ripe. Pick one whose underbelly spot shows its age. I have not had much luck with tapping or squeezing.