Summarize:

Sweet plantains give a little when you press them. Their skins are mottled yellow and brown. If you find green plantains, give them several days to ripe before you make your sweet dessert dish. Use a paring knife to chop the ends off the plantains. Use your fingers to pull back the peel and remove it from the fruit inside. Discard the peel. Lay the plantains on a cutting board and slice them into 1/2-inch pieces. If you like thicker plantains, slice them into 1-inch pieces. For thin, crispy plantains, slice them into 1/4-inch pieces. Pour the oil into a stockpot or frying pan so that it rises up the sides 1⁄2 inch (1.3 cm). Heat the oil until a deep frying thermometer reads 340 degrees. For a less oil-heavy dish, add just a bit of oil to a frying pan and heat it until it sizzles when you add a bit of plantain to the pan. Lay them in the hot oil and fry them until they're brown and crispy on one side, which should take about 2 minutes. Flip them over and fry them on the other side until both sides are golden brown. The longer they fry, the sweeter they'll taste. Remove them from the hot oil and place them on a paper-towel-lined plate to drain completely. Sprinkle them with sugar and cinnamon to taste. For a truly delectable dish, make a fresh batch of  whipped cream to top the fried sweet plantains.
Pick out ripe, sweet plantains. Peel the plantains. Slice them on the diagonal. Heat the oil. Fry the plantains. Drain the plantains. Serve them hot with sugar.