When you say tarnished, do you mean #2 or #3 in the picture below?
If it's #2, that's fine. Copper will do that after a while and beyond repeated treatment with acids which eat away at the oxide layer to reveal bright copper underneath, there isn't much that can be done.
If it's #3, then you do need to clean it off. That's corrosion, not tarnish, and the best way to sort it is to soak it in an acid bath like white grape vinegar. Find the cheapest one you can and work in a ventilated area as vinegar isn't fun to breathe. You can scrub it with a mixture of salt and vinegar, enough salt to make a paste, to take most of the corrosion off before soaking for a couple of hours in vinegar or until it is shiny. Some online guides also suggest adding salt to the vinegar bath to help speed the process up.
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