This is similar to a previous post:
http://www.able2know.com/forums/viewtopic.php?t=31704
First find one person who is not the random guy.
Call them A, B, and C. Ask A, "Is B more truthful than C?" If the answer is yes, then C is not the random guy. If the answer is no, then B is not the random guy. This can be verified by examining all possible permutations. Note that you don't know the identity of anyone at this point. You've only identified one who is not the random guy.
Let's say we determine that B is not the random guy. Ask B, "Would the other non-random guy say you always tell the truth?" If B says yes, then B is the liar. Otherwise, B tells the truth. Now you know the identy of B.
Ask B if A is the random guy. There are four possibilities:
B is the liar and says yes
A: truth teller, B: liar, C: random
B is the liar and says no
A: random, B: liar, C: truth teller
B tells the truth and says yes
A: random, B: truth teller, C: liar
B tells the truth and says no
A: liar, B: truth teller, C: random
This assumes each knows the identity of the others.