For an item to be considered silver -- or "solid silver," as it is often called -- it has to contain at least 925 parts pure silver per thousand. Silver plate is a cheaper process used to emulate the look of solid silver. There are two kinds of silver plate -- electroplated nickel silver, or EPNS, and Sheffield plate. Sheffield plate was the first silver-plating process. A lump of copper was sandwiched between two smaller lumps of silver, and all three were rolled in mechanical presses until they were only millimeters thick. In the EPNS process, a thin layer of silver attaches to a nickel base through an electrochemical process. Sheffield plate was made between 1775 and 1840, at which point EPNS took over. It's worth noting the difference, because Sheffield plate is much more scarce than EPNS, and thus more collectible.
Look for any marks on the piece. Solid silver should carry an assay mark to prove that it reaches a legal standard. This will be a numerical mark such as "925" or a symbol such as the "lion passant" -- a lion walking in profile -- on British silver. EPNS will have the letters "E" and "P" for "electroplate" and possibly "A1" for high quality. Most Sheffield plate will be stamped with a maker's name.
Inspect any raised decorative features on the item. Look for a blurring in some of the detail, almost as if it has melted. This is a sign of the softness of solid silver. If this isn't what you see, continue to the next step.
Inspect the piece for other signs of wear, paying particular attention to the tops of lids, edges and any other areas that might suffer from repeated polishing. To identify silver plate, look for places where the thin layer of silver has worn away, revealing the base metal underneath. If the exposed base metal is a pale yellow, then the item is EPNS. If you see a chestnut color, then you're holding a piece of Sheffield plate, which is likely to be somewhat more collectible than EPNS, although not as sought after as solid silver.