Chessmasters tug at their strings of influence, patiently move their pieces into places that often seem harmless or pointless until the trap is closed, and get innocent Unwitting Pawns (Who else?) to do all the heavy lifting. The best will also have layers upon layers of misdirection and backup plans in case some unexpected hero appears to gum up the works. They take the (very!) indirect route in order to snake through holes in their opponents' defenses without a trace... assuming they can refrain from boasting of their cleverness near the hero with a triumphant sneer and a raised eyebrow.
One obvious sign you're dealing with a Chessmaster is that, when he's gotten familiar enough with the heroes, he'll start breaking out the Xanatos Gambit by arranging a no-win situation for them. Any sufficiently-complicated cons or capers are also the MO of these types, especially if used regularly. Finally, anyone who successfully executes a Gambit Roulette is by definition a Chessmaster but be sure to establish their creds before this or the audience is likely to call Mary Tzu.
Many chessmasters are Villains With Good Publicity, but they can also be someone no one has ever heard of. Almost all Ancient Conspiracies are led by a collective of chessmasters, silently working toward their goals over generations.