Linda...Just spray the weed killer on the weeds being careful not to get on the flowers. My husband does mine!
I dig out by hand. So does my girlfriend and her "garden" is just under an acre.
Remove the weeds in the spring when they are little. Once the area is clean, put down Preen Weed Preventer as instructed on the container. I do this to mine, both vegetable and other gardens. I spend maybe five minutes per garden a week taking care of the pesky Creeping Charlie that comes in at the edges. It has never harmed any seeds that I plant in my veggie garden, it just prevents weed seeds from germinating, much like the weed and feed used on lawns in the spring, It keeps most seed born weeds from coming up at all. I just saw and advertisement that they now have one that lasts six months, but I only need to apply it once in my garden with the shorter growing season in Minnesota. Using the Preen probably saves me three or four hours of weeding a month in my gardens.