Bring water, salt & sugar to boil. Add the potatoes as soon as they're prepped, and cover the pot & let it cook at a slow simmer. The time will depend on the size of the potatoes. Check at about 10 minutes and judge the time from there. Unless you used red potatoes that are fairly large, it should not be more than 20 minutes.
Add the beans; bring to a full boil for about 7 minutes. Beans have to be done..but not over done, they have to still be bright green.
Drain the potaotes & beans and then return them to the pot. Leave pot on heat for a couple of minutes to reduce excess water. Add garlic & butter, and salt if needed to taste.