Old, mismatched silverware may not have a place at your table, but it's a great material to use to make your own silver jewelry without needing extensive metalsmithing training. Use silver or silver plated flatware, not stainless steel. Look for marks on the silverware identifying it as sterling -- a common marking is "925." If there is no marking, try the magnet test; if it is attracted to the magnet, it's not silver. The silver should be clean, but don't worry about tarnish while you're working with it, as it will need to be cleaned and shined when it's finished.
Full pieces of silverware are too heavy to use to make earrings, so you'll need to do some cutting. The very end of the handle or even the prongs of a fork make interesting-looking earrings that are simple to create. Clamp the silverware piece into a vise and saw off the desired piece using a jeweler's saw. Grind and sand the cut area with a rotary tool and sanding bitsw, then use a drill or rotary tool to drill a small hole in the piece, close enough to the edge that you can pull a jump ring through it. Attach an earring hook to the jump ring to finish.
A silverware necklace displays a whole piece of silverware around your neck, for pieces you don't want to cut up -- but that you don't mind drilling holes into. You can use the piece as is, pound it flat, or bend it into a U shape. Drill a hole into each end of the piece, then attach silver jump rings into each. Loop the jump rings into the ends of a silver chain that's been measured out to your desired length. Solder the rings shut with a soldering iron.
Silverware rings are a common craft show item that can be made at home simply using your own pieces. Wrap a string around the base of your finger and mark the end with a marker. Use the string as a guide for cutting the piece from the end of the handle, using a jeweler's saw or a rotary tool with a cutting tip accessory. Grind and sand the cut end, them place the piece over a metal dowel or ring mandrel that's about the same diameter as your finger. Pound the silver around the dowel or mandrel using a wood or rawhide hammer.
Silverware brooches can be made from just the handle, just the head or even the whole piece. Tiny pieces, such as pickle forks or sugar spoons, make pretty brooches just by attaching a pin back to them. For something more elaborate, use the bowl of a spoon as a surface for painting or creating a tiny diorama inside, or pound it flat and shape it. You'll need to solder the pin backs on for the best results, though hot glue will work, at least for a while.