Mix 1 teaspoon of dish soap into a cup of warm water until fully dissolved. Dip your wedding band in the solution and use a soft cloth (or soft bristle toothbrush) to gently scrub clean. Rinse with clean water and let dry on a clean, soft cloth.
Please be careful to not use any soap that contains beads or exfoliants. And also be careful to not rinse your ring over an open drain in a sink, should it slip out of your hands and fall.