Instructions
Look for chairs of slender proportions, with only the most restrained carved decoration -- for instance, a little reeding (a corrugated effect) on the arms. Such chairs could belong to the Federal Period (1785 to 1800) or earlier. The furniture of this period shows a strong English influence which of reflects an avoidance of anything too fussy or showy. If a chair looks so delicate you hesitate to sit on it, then it could well be a Federal piece.
Watch for any Grecian influences -- chair-backs in the shape of lyres, dining chairs that mimic the profile of ancient thrones, applied gilt laurel leaves. These would suggest that a chair comes from the Classical Period (1800 to 1840.) The style didn't derive directly from Greece but from Imperial French influences, which in turn drew on Classical originals for inspiration.
Assign any chairs that are especially exuberant and highly decorated to the Revival Period (1840 to 1890.) This was essentially an "anything goes" era of American chair-manufacturing when a whole host of styles ran concurrently -- Gothic, rococo, renaissance, French. The one thing all these styles have in common is an almost theatrical ostentation. Upholstery is often deep-buttoned with heavy fringes. Furniture from this period was made robustly and in large numbers, so if you own an antique chair there's a good chance it dates to this time.
Watch out for simple, unadorned chairs of an exaggeratedly angular design. These belong to the 1890 to 1940 period that culminated in the Art Moderne -- now usually known as Art Deco -- movement of the 1920s.