Take her costume jewelry shopping at the local mall. Tell her you want to buy her a gift and have her try on some rings. Test out various rings on different fingers noting which one fits her ring finger best and casually ask for the size or buy it when she's not around.
Get her friends to help. Next time they are having a girls night out have her friends bring up rings and ring sizes. Have them try on each others rings and note which one fits the best. Borrow the ring that fits best and take it to your local jewelry store for sizing.
If she has a ring that she already wears on her ring finger, grab it next time she takes it off to do some messy work or shower. Lay the ring on a piece of paper and run a pencil around the inside of the band and take your drawing to a jeweler. You can also make an impression of the ring by pushing it into a soft bar of soap.
If she's a deep sleeper, wrap a piece of string around her ring finger and mark the point of intersection. Measure the string against a ring size chart or take it to your local jeweler.