We're lucky - mailing jewelry is far easier and cheaper than mailing most other types of artwork! Most jewelry is small and lightweight enough to fit in the smallest size shipping box or bubble-padded envelope, and sent with a relatively small amount of postage.
When shipping jewelry, I package the piece carefully in a ziplock jewelry bag and place it (along with its hang tag or earring card) in a cotton-padded cardboard or metal jewelry gift box.
Then I slip an elastic bow onto the box and slide a blank gift card under the elastic, to make the jewelry easy to give as a gift. Or if the customer ordered the jewelry for herself, then my packaging can make her feel that she's just received a gift from herself!
Then I put the gift box, my packing slip, a few business cards, and any promotional flyers inside a medium-sized ziplock jewelry bag so none of these elements can be missed or thrown away accidentally when my customer opens the shipping box.
Finally, this package goes into a small bubble mailer or cardboard shipping box.