In a 4-quart saucepan, bring the water and smoked turkey to a boil over high heat. Reduce the heat and simmer, covered, for 1 hour.
While the turkey is cooking, wipe the collards with a damp towel, then wash 2 or 3 times or until all the dirt and grit has been removed. Chop the greens into 1/4-inch pieces; you will have 10 cups of chopped greens.
Add the collards, oil, salt, black pepper, sugar and red pepper flakes to the saucepan. Return to a boil, reduce the heat and simmer, covered, for 30 minutes longer. Discard the turkey before serving, or chop the turkey meat and add it to the collards.