If you simmer milk with acid, the milk will curdle. I wouldn't go this way.
If you insist on a sweet application, you have to add sugar (or another sweetener) to the mango. A sweet taste will cover acidity perfectly. You can either cook it with sugar syrup, or macerate it. After that, pureeing is probably best, because you want to avoid hard sour pieces in sweet sauce. From then on, your fantasy is the limit. Jam (maybe in combination with another fruit - how about that nectarine and some Grand Marnier?), sorbet, candy, yogurt-based smoothie, jello in molds or as a cake layer, mixing with cheese to create a spread or a mango cheesecake - everything is possible. The taste, however, will be less than optimal, because unripe fruit is not only sour, it doesn't have yet its full aroma. Still, it will work - not as well as a ripe mango, but it will be OK.
Sweet isn't the only option. The classic use for an unripe mango is to put its sourness to good use and prepare a mango chutney. Again, you can stay traditional and make it pure, or experiment with additional fruit and spice combinations. Then use the chutney as a dip or sauce in savory dishes.
I look for a few things...
- Colour: There are many different varieties of mangos. Some go from green to red, some end up Orange, some start off yellow and end up orange. So once you're familiar with the type of mango you're buying, you can get an idea of what a ripe one looks like.
- Smell: A ripe mango will smell sweet. Check near the stem end, the smell should be stronger there. You should smell it and think "mango". Smell is a large part of your taste, so it should be very familiar.
- Firmness: Mangos, like peaches will soften as they ripen. Just as it starts to go from firm to soft, it is just about ripe.
- Weight: With most fruit you can tell their ripeness by their weight. A riper fruit will be slightly heavier than an unripe one.
As an aside, if you're at a grocery store, and you see a few different types of mangos, look for these Ataulfo mangos: http://goo.gl/IeEZ4. They're my personal favourite. The flavour is richer, and they are a lot less stringy.
Finally, DO NOT refrigerate if you want them to ripen.
More info on the Ataulfo mangos. (There is also some generic mango info there)
Best Answer
I haven't tried this before but I found this youtube video that shows you how. Cut into the mango, starting where the stem was and going around the long way, just in to the pit. Reach in with a spoon and scoop around the pit, separating one half of the mango from the pit. Then scoop the pit out of the other side.