Depending on your skin chemistry, jewelry can sometimes tarnish a bit.
Mix a small amount of mild “dawn” dish detergent with warm water in a bowl. Put the jewelry into the bowl and let sit for a few minutes. Use a soft toothbrush (like a baby tooth brush) to gently scrub the jewelry. Remove item from soapy water, rinse it and dry thoroughly with a soft polishing cloth.
You can also use a polishing kit for extra shine and to remove any tarnish. You can also bring your your jewelry to a reputable jeweler and ask if they can put your piece in their ultrasonic cleanser. A small at-home ultrasonic is also a great, fairly modest investment, especially if you are very keen on keeping your jewelry at its most sparkly.