If it gets sticky, then it's shellac. Polyurethane, shellac, varnish and lacquer: use a cotton swab with acetone and apply it to the wood. If it gets sticky, then it's shellac or varnish and if it forms balls, it has a polyurethane finish. If it is lacquer, the lacquer will completely dissolve.
One way to test the film-forming finish is to see if any films have formed. With a very sharp blade, such as a multi-purpose razor, scrape the surface in an inconspicuous area. You'll see white, whitish, or even pale yellow, plastic-like chips without damaging the real wood. White will normally mean urethane, shellac, or water-based lacquer.
Additional solvent testing will help identify them more specifically. Off-white can be a urethane modified with oil, lacquer or amber lacquer. Pale yellow would probably indicate mast varnish, alkyd varnish, or other oil varnishes. It would be difficult to differentiate even more between these varnishes.
If it scratches and immediately gets on the surface of the wood, it will most likely have a penetrating finish, since there is no film on the actual surface. To find out what type of finishing treatment your furniture has, you can try a discrete area of the wood, such as the upper inner part of a leg.