References for homotopy colimit
Dan Dugger wrote the following intended for grad students (just a draft - not on the arxiv yet): http://www.uoregon.edu/~ddugger/hocolim.pdf
(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.
Chris Douglas has a nice short discussion of homotopy limits in his text “Sheaves in homotopy theory” (Chapter 5 of Topological modular forms).