There are a lot of products on the market, for cleaning Silver theses days. Most of which are full of chemicals and can be quite harsh on your silver. I've found the dip solutions do get your jewellery clean, but they tend to take a lot of the shine away from your silver.
I was given a tip a lot of years ago , and i've been following it ever since.
All you need is an old toothbrush, with soft to medium bristles, put a pea sized amount of toothpaste onto it. Gently brush onto your jewellery, the toothpaste will go a greyish colour if the silver is really dirty. Give it a good rinse, and dry off with a soft cloth. Your silver will look sparkling clean straight away. Even if your silver is just looking a bit dull, this method will give it that just new look.
I also use this method for cleaning my copper and brass jewellery.