Simply rinse the piece of jewelry and gently scrub the tarnish or dirt off the surface with a soft cloth or toothbrush, be sure not to scratch the metal or stones with a rough surface.
Rinse again in the warm water, then dry and polish to a beautiful shine.
For other metals with no gemstones, add 1 part ammonia and 1 part dish soap and soak in warm water. Scrub with soft cloth, rinse. dry and polish for a lovely shine.
You can use denim (jeans) or simply a polishing cloth to shine tarnished jewelry if your resources are limited.
Caring for your jewelry also includes; taking it off when you shower, clean house and even sleep. Be sure to put it away in a safe place away from dust and moisture. It will last much longer and stay looking new.
If you have any questions about specific jewelry, please comment and I will be sure to respond.