A custard apple is ripe when you gently squeeze it and it gives slightly under your hand. Much the same as an avocado. You can buy custard apples ready to eat, or still hard to the touch and let it ripen over the next few days after purchase.
If you want to hasten the ripening process then simply put the fruit into a brown paper bag with a banana and leave it on the kitchen bench. The banana will accelerate the ripening of the custard apple.
Custard Apples are only eaten when soft, and only the flesh is eaten. To eat, simply cut in half and scoop out the white flesh. The Custard Apple should be moist with a pleasant sweet aroma. Once ripe, custard apples can be stored in the fridge for up to 3 days. Once the skin has gone purple or black, they have passed their best eating quality.