just scrub with some baking soda may need to use stiff toothbrush to get into all edges inside and out rinse, dry really well so salt and pepper doesn't stick to them.If your in high humidity area put a few grains of white rice in salt shaker keeps salt from clumping.
Are they stainless steel, aluminum, or silver?
Since it's tarnished, I'm assuming silver. Soak in boiling water, aluminum foil, and baking soda. Dry. Apply toothpaste and buff clean.
Try baking soda on a lemon wedge. Rub against the metal, then wipe with clean, dry cotton cloth.
Thank you all, my shaker tips looks shiny and new!