The etiquette books won't tell you this, but the best way to eat a mango is to go to Tulum on the Caribbean coast of Mexico and find a little cabaña to stay in. Once you're a bit sunburnt and have sand in your hair, take a taxi into town, 40 pesos plus 2 to 5 pesos tip, and ask the driver to drop you off in front of the frutería that has a mural of Adam and Eve painted out front.
Pick one or two of the nicest, ripest mangos you can find. The flesh should give in generously to your thumb when you press it, and the color should be a blushing orangey apricot. A bruise here or there is a mark of character and will do no harm to your experience.
Once you've made your way back to your cabaña, find a sandy spot in the sun or shade, as you prefer, but close to the water so you can hear and see the waves. Be sure to wear a swimsuit or less.
Then take any kind of knife that comes to hand—the Swiss army knife that always travels with you, or a sharp chef's knife or a dull-edged butter knife you stole from the last hotel you stayed in—and plunge it into the point where the mango has been snapped from its stem. Run the blade all around the fruit's circumference, creating two halves, and cut into it deeply enough so you make contact with the pit of the mango. Allow the juice to cover your hands and drip down your arms into the sand, where a little family of ants awaits any bits of pulp you might share with them.
In whatever sloppy way you can manage, split the mango in two and give one half to a friend so you can laugh at how messy your faces have become as you suck up the sweet mango flesh. Scrape up any remaining flesh on the inside peel with your teeth and never mind if long stringy bitrs get caught between your teeth. When finished, pat your hair back into place with your sticky fingers, walk to the water's edge and dive in.