TITLE: Simplicial homotopy book suggestion for HTT computations
QUESTION [19 upvotes]: I'm struggling through Lurie's Higher Topos Theory, since it appears that someone reading through the book is expected to be somewhat comfortable with simplicial homotopy theory.  The main trouble I've had is computing things like the join, product, coproduct, pullback, pushout, and so forth.  I understand them as far as their universal properties, and maybe have a little intuition because the category of simplicial sets is a presheaf category over the simplex category, but Lurie uses geometrical language, so I can't even compute like when working with presheaves.  So, could you lot recommend some books or lecture notes, preferably with suggested sections, that won't go too deep into simplicial homotopy theory, but deep enough for me to learn how to compute?
Note: Most of the time I waste is sitting around with that book is trying to make sense of the computations, while I understand the arguments just fine.  So please, don't suggest an entire book detailing all of simplicial homotopy theory from start to finish.  I have a goal in mind here, and I'm only trying to learn as much as is necessary for me to continue reading HTT.

REPLY [5 votes]: Echoing what Urs said, "But you should all be using the nLab more: if you want literature on quasi-categories, look up the references section on quasi-categories! :-) " and in regard to your question in particular, "See the nLab page on simplicial sets for links."
By looking at this nLab page on simplicial sets, in the references section you'll have found (as of this date, July 21, 2011 10:19 pm, EST):
Greg Friedman: An elementary illustrated introduction to simplicial sets 
which is chock full of pictures illustrating the geometric ideas underlying the combinatorics of simplicial sets. As Friedman discusses in the introduction on the second and third pages of  this paper, 

"Here, for the most part, you won't
  find many complete proofs of theorems,
  and so these notes will not be
  completely self-contained. Rather, I
  try  primarily to show by example how
  the very basic combinatorics,
  including the definitions, arise out
  of geometric ideas and to show the
  geometric ideas underlying the most
  elementary proofs and properties."

Suffice it to say, those notes may be the end of your search in finding a concise introduction to simplicial sets that also helps develop your geometric intuition and the computation of products. You also might find the references I gave in answer to the question here helpful.