What you do: You're going to use your middle finger and your thumb and make a flicking motion like you're flicking a large crumb off a table. Holding the apple between the thumb and middle finger of your other hand, gently flick the apple with your fingernail. (There's no need to do it hard; you'll bruise the apple. Just enough to make the apple ping a little.) The apple's going to make a noise, a musical note if you like. The riper and juicier and crisper the apple is, the higher and clearer the note. If the apple makes a sort of dull "thwock" or "thunk," it's going to be mealy.
You want to select apples that are of a roughly equal ripeness (based on how they look): apples that are unripe are going to make a substantially different noise compared to apples that are ripe. Also consider that some apples that are getting a little older, ones where the skin may even be a bit loose or wizened, may still be very edible indeed, even though they don't make the same high note. (You may notice a difference in clarity of the note they make, though.)
This will take a little experimenting to get the rhythm, but it's not Big Science, so it won't take you long at all. When I am selecting apples at the store, I usually have two or three in hand that have the highest notes, replacing with apples with higher notes as I go, until I get the feeling for what the highest note I'm going to get from that bin is, then I start bagging them. And yes, I get very good apples this way.