I use silver dip, drop the jewellery in the dip, wash the dip off in cold water, dry with a fibre free cloth, then polish with a silver cloth
Silver is best kept in the dark when you are not wearing it to prevent tarnishing happening so quickly.
Here are some other options (I have never used them so can not recommend them)
Boil it in baking soda in a pan on the cooker (that sounds scary if you had stones with with glue they would be stones no more!)
Wash in diluted woolite
Aluminium foil & vinegar (no no no no!)
Rubbing alcohol – this could work, I clean my glasses with vodka and they sparkle