Most story games by LucasArts were written using the SCUMM system.
Monkey Island 2 is one of them.
There is a very nice cross-platform SCUMM interpreter called Scummvm (http://www.scummvm.org) which will run, among other things, Monkey Island 2. If for some reason ScummVM does not work for you, it still is possible to run MI2 and other old DOS games through a utility called dosbox (http://dosbox.sf.net).