I don't remember where I learned this but every time I cut a mango, I think, "The world needs to know about this trick!" And so, I took pictures as I cut up yesterday's mango.
Using a paring knife, cut top to bottom, slightly off center. There is a giant pit, or seed, in the center. Go slow and feel your way around the pit. If you feel there is too much resistance going clockwise, then try the counterclockwise.
Then score it again perpendicular to your first cuts.
Repeat with the second half.
Because I don't like wasting any food, I scrape the pit as clean as possible.
Remove the remaining skin - as you would peel an apple or potato.