Simply cut the onions down very close to the white part and place in water (make sure to change the water every couple of days). After about a week they'll be a good size, and you can use them as needed. If they start to grow too big, just trim them down to ensure they continue to grow. They won't last in water alone forever, but should keep growing for a month or so.
They also make a nice addition to a kitchen windowsill!