For any one curious, 'ಠ' is pronounced as 'Ta' (Kannada language) :)
If you wish to make the sound, position your tongue like you're trying to stick it down your throat. The bottom of the tongue should be touching the top of your mouth. Then, make a "tuh" sound. If you do it right, it should sound hollow and "harder" than a normal Englilsh "t" sound.
The letter is SHIFT + ' (or just ") to yield ಠ.
Unfortunately, you apparently can't do it on OS X without bringing up a menu and/or changing your keyboard layout: http://en.wikipedia.org/wiki/Unicode_input#Hexadecimal_code_...