How to pick a good mango at a local store?
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)