Polish your dish to uncover any obscured engravings or patterns.
Look for signs of the word "sterling" or the numbers "925" or "92.5" -- all are clues that the silver dish is sterling.
Look for the words "silver plated" on the item, if you don't see indications of it being sterling.
Try the magnet test. If you touch a magnet to the dish and the magnet sticks to the dish, the dish is definitely silver plated and not sterling. If your magnet does not stick, that does not necessarily mean that the item is sterling; it could simply mean that the mix of metals underneath the silver plating is not magnetic.
Try a silver acid testing kit. You will have to make a small nick on the dish, in an inconspicuous area, and put one drop of the kit acid over the nick. The color that the acid turns qualitatively indicates the amount of silver in your dish. Kits will come with charts to help you match color to silver content. Unfortunately, you will have to damage your dish a bit to use one of these kits.