How does Eugene Ionesco's "Rhinoceros" demonstrate qualities of existentialism?Existentialism itself is hard for me to grasp, if anyone could...

I think that you have a couple of challenging elements
here.  The philosophy is a bit complex and that is only matched by the Ionesco work. 
Between both of them, one can get lost in the realm of inquiry.  To break things down, I
would suggest that one can think of existentialism as an  actor being thrust on stage,
in front of an audience, spotlight blaring, without a script or without a director with
the order "to act."  In this light, the individual is forlorn, without any sort of
relief, and is isolated from all others in their lack of totality and explanation as to
why things are the way they are.  All the individual can do is "act."  In the end, this
is how existentialists see the world and the human being's place in it.  This might
connect to Ionesco's play in a couple of ways.  Berenger's stand against the rhinoceros
reflects how he stands alone against a social order and can "only act" or use his
freedom.  The alienated and isolated nature of human beings with only the agony of
choice to accompany them is something that we see Berenger embody when all of his world
turns against him and he is the only one left.  In his resistance as being "the last
man," he has only his freedom and this is what might make Berenger an ultimate
"existentialist" hero.