Wash the greens in a sink filled with cold water. Drain greens and wash a second time. Drain greens and cut away any heavy stems (optional). Cut leaves into bite-sized pieces. Set aside.
In a large skillet or 3-quart saucepan, cook bacon until lightly browned on medium heat (or heat 1 tablespoon of bacon fat). Add onions, cook over medium heat 5 to 7 minutes, stirring occasionally, until onions soften and start to brown. Stir in garlic.
Add water to the hot pan, stirring to loosen any particles from bottom of pan. Stir in sugar and red pepper. Bring mixture to a boil. Add the beet greens, and gently toss in the onion mixture so the greens are well coated.
Reduce heat to low, cover, and simmer for 5-15 minutes until the greens are tender. Stir in vinegar. (For kale or collard greens continue cooking an additional 20 to 25 minutes or until desired tenderness.)