References for homotopy colimit (1) What are some good references for homotopy colimits?
(2) Where can I find a reference for the following concrete construction of a homotopy colimit?  Start with a partial ordering, which I will think of as a category and also as a directed graph (objects = vertices, morphisms = edges).  Assume we have a functor $F$ from the graph into (say) chain complexes.  We will construct a big chain complex (the homotopy colimit) in stages.
Stage 0: direct sum over all vertices $v$ of $F(v)$
Stage 1: direct sum over all edges $e$ of the mapping cylinder of $F(e)$, with the ends of the mapping cylinder identified with the appropriate parts of stage 0.
Stage 2: direct sum over all pairs of composable edges $(e_1, e_2)$ of a higher order mapping cylinder, with appropriate identifications to parts of stage 1.  This implements a relation between the three stage 1 mapping cylinders corresponding to $e_1, e_2$ and $e_1*e_2$.
Stage 3: direct sum over all triples of composable edges $(e_1, e_2, e_3) \dots$
 A: Chris Douglas has a nice short discussion of homotopy limits in his text “Sheaves in homotopy theory” (Chapter 5 of Topological modular forms).
A: A good (if kind of old) reference is Vogt's "Homotopy Limits and Colimits". I can't find a free reference for it, but if you can't access it, I could email a pdf (if that's allowed here).
Also, in the IMA's video library there's a video of Gunnar Carlsson giving a talk on homotopy limits & colimits. http://www.ima.umn.edu/videos/?id=870
A: I'm way late on this one, but for the record I'll point out that a nice answer to question 2 can be found in Hatcher's Algebraic Topology book, Section 4.G.
A: Some useful information is in 
Chacholski, Scherer, Homotopy theory of diagrams, arxiv math/0110316 
This and further references with useful material are listed in the reference section at nLab: homotopy limit. 
(By immediate dualization this applies to homotopy colimits, of course).
A: I found the following exposition by Emily Riehl very useful:
http://www.math.jhu.edu/~eriehl/hocolimits.pdf
A: I have learned a great deal from Emily Riehl's book, Categorical Homotopy Theory. At the time of this answer a (possibly outdated) pdf is hosted on Emily's website, here. Chapter 6 is full of useful information. I also enjoyed the examples in section 8 of her paper The Theory and Practice of Reedy Categories with Dominic Verity.
A: I learned today that Pascal Lambrechts also wrote a short primer on homotopy limits and colimits, filled with good exercises. It is online here (for now).
A: My answer may be a bit late, but E. E. Floyd and W. J. Floyd: Actions of Classical Small Categories has helped me understand some of these concepts.
A: Dan Dugger wrote the following intended for grad students (just a draft - not on the arxiv yet):  http://www.uoregon.edu/~ddugger/hocolim.pdf
A: (1) I happen to like this paper, but of course I'm biased.  (I hope self-citation isn't forbidden here...)  However, I started writing that paper mainly because I couldn't find an existing reference/introduction that I liked.  So if someone has another reference to suggest I would love to hear about it.
(2) This sounds like the simplicial bar construction, which is the one I used in my paper above.  I think I included some other references in the bibliography.
