I can't say I'm an expert, but I do grow a few every year. One trick is to look at the tendril that comes off the vine near the fruit - it will dry up as the melon ripens.
The tapping on it and hearing a hollow sound is also pretty reliable once you have a trained ear, so start thumping all of them to get used to the sounds. When they're ripe, the skin is stretched like a drum, which is what gives it the sound - too ripe, and I've actually had them crack when I tapped (those were still fine to eat, but don't keep outside the fridge).
