trying to get the copper part shiny again
A lemon sliced in half dipped in salt is a great non chemical treatment for copper and cheap!
soak in toamto juice takes dirt off
cameo anti tarnish cleaner for stainless steel copper brass and aluminium
Try SOS or Brillo pads...
Use copper polish. The powder form will get them shiny with a minimum of effort and isn't too hard on the copper. You will need to dry them, because otherwise they'll just tarnish again immediately. My mom has copper bottom pots, which she's had for at least 40 years. This was just part of the ritual. Wash, polish bottoms, dry them (at least the outside), and put them away. If you wash them in the dishwasher, you could polish the bottoms before you put them away. You won't necessarily need to do it every time, but I don't think there's any way to keep them from tarnishing so you will have to do it regularly.