Look at what rings and jewellery she normally wears - is it dainty or chunky? What kind of shape is the band - wide, small, thin? What type of metal does she normally wear i.e. yellow gold or white metal, etc. Take mind notes but be tactful. You could always ask a close but trusted friend of hers to help you choose.
Don't worry if she doesn't usually wear rings - you could always find out what her favourite earrings or necklace are and choose something that goes with these. There are numerous ways to secretly find out her ring size, this may include seeing which of her friends has the same size finger as her, trying her ring on your fingers to see which one it fits or where on your finger it fits.
Or you could go shopping together, and take interest in what she is pointing out. If you are still concerned you could always wait until you have proposed and choose together. Some people use our sample/replica engagement rings to pop the question (though, of course, we need these back!).