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.
Chessmasters can sometimes be on the side of good, but if so they'll almost certainly be the Anti-Hero (the Pragmatic Hero variation) at best or the Well-Intentioned Extremist at worst, as it's very hard to plan a Chessmaster scheme that doesn't sacrifice a few pawns along the way. Heroic Chessmasters are very often introduced as a Mysterious Employer. The Svengali, in acting for the (supposed) good of his protégés, will often be this (and if he is not, he will pretend).
Chessmasters can occasionally be The Strategist, although given the volatility of war, most Strategists will only ply their schemes one campaign at a time, with an emphasis on short-term goals (and an eye towards all possible future contingencies). The Game Master may be a Chessmaster also, but many of them prefer to give their orders more directly. Many chessmasters are Villains With Good Publicity, but they can also besomeone no one has ever heard of. Almost all Ancient Conspiracies are led by a collective of chessmasters, silently working toward their goals over generations. Chessmasters also tend to beoverconfident and usually panic when their "perfect" plans fail. The exception to this is when Magnificent Bastard and Chessmaster overlap, since a Magnificent Bastard is quite good at rebounding from defeat. Fond of a Battle of Wits.
Of course, actual chess ability is implied, and some Chessmasters take it literally, mapping their plans out with an actual chessboard, occasionally with pieces shaped like the main characters. Don't ask how this works, or where they get pieces. This is most likely a result of Smart People Play Chess. Compare the Manipulative Bastard who tends to be more personal and controlling in her/his manipulations. Compare/contrast Opportunistic Bastard as well.
Chessmasters are usually (but not always) non-physical and unsuitable for action due to age, infirm, or simply being a thinker, not a fighter.