Look under the term "cryptanalysis"
The most "common" way of breaking encryption is brute force attack. Basically you try every single possible combination of keys until you find the correct one. That's basically what they do in the DES or RC5 challenges. In your case study, probably it'll be more appropriate to do find the password by trying every single word in the dictionary.
For certain algorithms, there're certain weaknesses in the design so that they can be broken in ways more efficient than brute force attack. I won't go into much detail here, you can always find info about them on the net.
Of course, the easiest way would be pointing a gun at the guy's head and force him to reveal the password
Have fun in the assignment!