This is how I learned how to eat a mango. In '95 and '96 I spent the summer in Guatemala. The Guatemalans are VERY adept mango eaters, even before they had the metal skewer/peeler method.

They take the fresh mango and roll it around in their hands until the fruit is soft. This frees much of the juice from the meat inside. they then bite a small hole (1/2 - 3/4" or so) out of the fruit with their teeth and squeeze the juice from out of this hole into your mouth. Then when all of the squeezable juice is extracted (most of which is in your belly and not on your face or hands) the meat is peeled piece by piece and scraped along the teeth to get it off. Then they gnaw and scrape on the inner pit until all of the juice and sweet fruit is extracted.

But I like to eat the skin, as it gives a nice sour/bitter contrast to the sweet fruit and it isn't all that bad, and it has a TON of fiber in it which is pretty good for ya anyhow.