There is no fool-proof way to determine if a watermelon is ripe without cutting into it.
The best you can do is look for certain signs:
Weight: A ripe watermelon consists of 90% water, so the heavier the better!
Size: It’s not necessarily true that a big watermelon is ripe, but if choosing between watermelons you might want to choose a relatively large one assuming they are from the same grower.
Sound: A ripe watermelon is dense and produces a deep hollow sound when you tap the outside with your knuckles. Compare with other watermelons and select the one that sounds/feels the densest.
Spot: A watermelon sits on the ground as it grows. There’s a spot on the melon where it contacted the ground. Find that spot. A yellow-colored spot suggests ripeness. A white or pale green spot indicates immaturity.