If a mango has subtle wrinkles, it's ripe and ready to eat. If you are looking at pre-cut mango, look for fruit that has a firm flesh rather than a slimy one.
A ripe mango has a little bit of give but does not stay indented when pressed. A medium-ripe mango is firm but not hard, while an unripe one is much harder.
The sweeter a mango smells, the riper it is. An unripe mango will have almost no smell, so it won't be sweet; no aroma means that it still needs some time to ripen.