How do you make the sweet fried plantains (and not ones that taste like potato chips)?

Ever been to a Cuban, Latin-American, or other kind of place and ordered plantains, and what has come out has been something more along the lines of a dessert...super sweet, dark or golden brown, so tender, where it almost melts in your mouth?

Well, I want to know how to make those.

I had one ripe plantain at home, and decided to experiment, but what I ended up with were hard, potato-chip like plantains, that seemed almost chalky. Maybe the secret is in the plantain, and I need to find a specific kind that will give me the sweet effect I am looking for? I've had plantains at a restaurant where they were more along the lines of chips or something similar, and that's just not for me. I like them sweet.

Any recipes, tips or suggestions are MOST welcome.