In a large saucepan or medium Dutch oven, cook bacon over medium heat until it has rendered most of its fat and has begun to brown, about 5 minutes.
Add the onion and saute until translucent, about 5 minutes.
Add the green beans and potatoes and enough water to just cover them.
Bring to a boil, then reduce the heat to low. Season with salt and pepper, to taste, then cover the pan and simmer until the beans are very tender, about 1 hour, stirring occasionally and adding more water if necessary to keep the beans covered.
As the beans get close to being done they will become quite fragile, so take care when stirring.