The most common stainless steels are the austenitic grades. These grades of stainless steel have a higher chromium content and nickel is also added. It is the nickel which modifies the physical structure of the steel and makes the austenitic grades non-magnetic. Other grades of stainless steel may be magnetic.
Solid brass is also not magnetic. If a magnet sticks, the item is usually steel or cast iron, with a brass plating. If the magnet does not stick, you can test further by scratching a hidden area with a sharp tool. If you see a shiny yellow scratch, the item is likely solid brass. If you see a silvery scratch, your piece is likely white metal (zinc). Iron, steel, and white metal can all be replated, in which case a lacquer is always applied to protect the plating.
Test with a grinder - sparks generally means stainless steel. No sparks means aluminum or chrome-plated brass. Use a grinder to grind off a section - if it is more yellow or gold colored, it's Brass.
If it is stainless steel, it will have a uniform appearance throughout. Cut or grind through the piece of metal to make sure it's not just chrome plated steel.