Who it works for: The practical one. You'd rather have a ring that suits your style than a big surprise.
How to do it: While walking past a jewelry store, casually express interest in stopping in and taking a look. Depending on the store, the salesperson will likely ask if you'd like to try anything on. A bolder option: Decide on a time to formally shop for rings together.
Timing tip: If your partner's a traditionalist, he/she may be opposed to shopping for the ring with you. If this is the case, consider going "window shopping" together, so there's no pressure to buy while you're out. That way, he/she can go back and buy the ring without you knowing.