How do you care for stainless steel jewellery?

Soapy water / Baking soda / White vinegar.
Regular cleaning can be done by soaking the jewellery in hot soapy water, rinsing with clean water and then drying with a soft dry cloth.
For a more intense cleaning, baking soda may be necessary.
Make a paste by mixing the bicarbonate with a little cold water, and rub your jewellery with a small brush and a little paste. Rinse with warm water and white vinegar. Drying should always be done with a soft, dry cloth.
Prohibit the use of abrasive materials which would damage the protective layer of your jewellery and could make it oxidisable.
Also avoid direct contact with perfumes which could cause your jewellery to tarnish.