When you plug the second monitor in, it'll probably default to mirror the first monitor. Right click on the desktop to get into monitor preferences and change it to extended desktop. You can set up what ever you like on the secondary by dragging the window over. The game will run on the primary monitor. Games can usually run in 3 modes: Windowed (can be sized), windowed (fullscreen), and fullscreen.
Windowed modes mean the game uses the preferences for the desktop for gamma, etc and you can just move the mouse in/out of the game making something else the active window.
Fullscreen mode - utilizes all of the graphics settings set in the game and you use alt-tab to switch in/out of the game to another window. This generally gives the best gameplay.
Power use: Unless you have an Nvidia GTX 6xx card, there's a significant idle power adder when you run two monitors. AMD and earlier Nvidia cards do not downclock the memory...Techpowerup
both show multi-monitor power use in their reviews.