Each game will tell you whether it will support 1 wiimote or many, by looking on the back of the box. If the game has more than 1 player onscreen at any time then the answer is fairly obvious, but the games that are turn based usually can be set up for either system.
The wiimote is the basic controller. It can be used alone (on some games) or by adding the nunchuk or the classic. The nunchuk and classic are not controllers in their own right, they are addons to the wiimote.