You can get it started off with some aluminum foil, baking soda, and boiling water.
http://scifun.chem.wisc.edu/HomeExpts/TARNISH.htmlRepeat as necessary to get mostly untarnished.
Then you can do another round and take a toothbrush to it (dip in baking soda mix) to get the grooves clean.
Lastly, shine it up if necessary with a polishing cloth. Wiping clean between foil+soda rounds with a soft microfiber cloth might also help.
Let us know if this helps. I've polished some heavily tarnished items this way, but nothing completely black.
LAstly, I've heard about the product Tarnx, a dip to clean liquid, but would try the simple foil and baking soda method because it doesn't take layers of silver off. Your item might only be silver plated and you have to be careful about polishing off silver with such items.