It depend on what it is made out of. I use silver polish on any silver items but otherwise I use a cleaner intended for jewelry I purchased from the jeweler that made one of my rings. I'd share the name but it was a proprietary product not intended for resale.

I'm sure other jewelers have cleaning products they recommend.

What kind of metal is it?

For sterling silver I have Diamond sterling silver cleaner. Takes 30 seconds. It last forever.

I have few pieces from Tiffany’s. The cute pouches they give don’t help the oxidation.

I guess if I then put it in a box as well, it might keep it at bay.

The brand I use for sterling silver is Connoisseurs. You just dip it in the container, rinse and dry. So easy...have used it for years.

Silver tarnish is silver sulfide, as the silver reacts with sulfur in the air. I have no idea how much sulfur is in the air, but evidently it's there.

For the aluminum + baking soda to work, I think all of the chain must be in contact with the aluminum. This might work better for larger pieces of silver.

Are such items ever plated and not solid? If so, could the plating wear or tarnish off?

It's sterling silver. Sorry, I should have mentioned that.

I use Hagerty's 'silver foam' on good silver and the 'dip it' stuff on the less valuable bits. The foam is applied with a damp sponge; it's a rub and rinse process. The liquid can be 'painted' on to pieces too big to dip, using a small c cloth. (The dip stuff stinks; be sure you have good ventilation and wear gloves.)

Try rubbing the chain with toothpaste, wiping gently with a soft cloth. Then rinse and wipe dry.

Jas, I use wright's silver polish and a soft sponge, then wash with soapy water and rinse. Not sure if you've got wright's there, but a good silver cream polish usually works. I've tried the aluminum foil and baking soda... you have to have it in boiling water the whole time to work, and then I find it leaves a weird film that's hard to remove. Once you clean it, keep it in a zip lock baggie. It won't tarnish as fast. SS with a little argentium in it tarnishes much more slowly, but it's hard to find.

Once it is cleaned, wax and polish it to slow down tarnish. A bit of automotive wax will do, but be cautious. Do not use a cleaner type that contains abrasives, It'll wear down the jewelry and can remove plating.

I've used automotive wax on my kitchen and bathroom fixtures. It creates a very good appearance. Periodic waxing the kitchen faucet was recommended on the instruction sheet that came with the faucet set.