The more red color it gets (and the darker the red turns) the more mature (ripe) the mango will be. This will also help tell you when your mango is becoming too ripe, which is also not great.
Ripe mangoes are soft. You can gently press against their skin with your fingers. The skin and flesh shouldn’t indent completely, but the mango should be soft.
If you are looking for a quick method, you can wrap the mango in a brown paper bag or newspaper. Leave it at room temperature.