No metal jewelry is completely tarnish free, so it's necessary to keep a few things in mind when purchasing and maintaining your jewelry:
My copper plated jewelry is cleaned and afterwards coated in various hard sealants and finish sprays to prevent oxidation and tarnish. Does this mean it will never oxidize? No. I do what I can to prevent this natural process, but eventually, it may require some care. Avoid wearing your copper jewelry with sunscreen and lotions. Copper is also not a metal that does well in water, so be sure to take it off before swimming or showering. This is especially the case with copper plated jewelry, as miniscule pores are still on the surface of the piece, even after polishing.
Here's what you can do with your piece at home: If your jewelry is just dirty and not tarnished, gently scrub it with a toothbrush and dishsoap. To remove tarnish, you can soak your jewelry for about 15 seconds in a mixture of salt, vinegar, and water, and afterwards scrub gently with a soft sponge that is dampened with vinegar.
Alternatively, you can use lemon or lime juice with salt for a similar effect, and rinse with water after.
Don't soak the piece longer than is needed, and avoid harsh scrubbing materials like steel wool.
If you are hoping to reduce how often your jewelry requires care, you may want to then recoat your piece. If you're going to do this, then I would recommend wearing gloves during the above mentioned cleaning process, and also for sealing. Even small amounts of skin oils left on copper can cause a piece to tarnish more quickly.
You can seal copper with 2 coats of regular clear nail polish, if you want a quick fix. At least 2 coats. The initial seal for all of my jewelry is Everbrite UV protective clearcoat. It comes in a kit with neutralizing liquid and a buffing pad. I also use shellac spray and clear gloss hard enamel spray.