This is really a pretty simple process. As others have said, bleach will work just fine. Soak the stem in bleach for a few hours, and when you take it out the stem will likely look and feel pretty nasty. Don't be alarmed! Just take a magic eraser (I've even had success with Brillo pads) and scrub the heck out of it for a few minutes. The oxidation will come off. Rinse the stem in water and then dry thoroughly. After that's done, take a few pipe cleaners soaked in high-alcohol spirits (like Bacardi 151, PGA, or Absinthe) and run them through the stem. Repeat this process until they come out completely clean. Last, polish the stem with extra virgin olive oil and let it dry. Your stems should look good as new after this process!
I also recommend polishing the stems with olive oil every week or two, just to keep them looking good.
Anyway, like I said, this is a pretty simple process once you get the hang of it.