I live in the north, and it's very clear to me that mangoes are not from around here. You can tell just by looking at them. The trees in these parts don't produce things that large. So when we buy mangoes in the grocery store, we're not likely to know if they're ripe and we don't really know how to treat them when we get them home.
If you've ever been in an area where mangoes grow, you know the best way to choose a mango is to find a ripe one hanging on a tree--not a likely sight at our local grocery store. Mangoes happen to be one of those fruits that does not tolerate early harvesting and long-distance shipping well.
There are two main types, large reddish green ones (up to eight inches long), and small yellow ones (three or four inches in length). Mangoes are quite soft when ripe, even softer than a ripe avocado. If they were picked green they will often turn brown inside instead of ripening, and in this case they have a very unpleasant taste. There's nothing to do when this happens except toss them into your compost pile.
When you're purchasing mangoes, it's a challenge to know what's going on under the skin but here's a tip that will help; dark spots or blemishes almost always indicate internal problems for a mango, whereas they will have a pleasant and fragrant aroma if they have ripened correctly.
If you purchased mangoes that are not soft enough to be ripe, and are not emanating a noticeably pleasant odor, put them in a brown paper bag with a couple of semi-ripe bananas. Bananas give off ethylene gas as they ripen, which is a gas used to ripen fruit in commercial packing plants. Ripe mangoes are such a taste-treat; it's certainly worth the effort to try ripening them. But the unfortunate reality is that mangoes picked too soon will never ripen correctly, so if you bought them green you always run that risk.
If you do happen to purchase completely green mangoes, I would recommend using those in your cooking rather than trying to ripen them. They will have a tart pleasant taste. You can dice them and mix them in with rice and vegetables, add them to soups, put them in a fruit salad or blend them to serve as a relish with meat.
Be sure at some point in your life, to eat a fresh ripe mango straight from the tree. There is nothing in the world that tastes so exquisite.