One traditional southern recipe for fresh turnip greens is to cook them in a pot of water and ham hock. First let the ham hock simmer in boiling water for about two hours. Then add fresh turnip greens and sugar and cook for an hour until the greens are tender.
Another method for cooking fresh turnip greens is to simmer them in a pot of chicken stock with other sautéed ingredients, such as bell pepper, onions and garlic. Then add salt, black pepper and sugar as seasoning. The turnip greens should be stirred every 15 minutes and should simmer for between 30 minutes and 2 hours, or until the greens are tender.