If one really wants to understand the formulas for how to construct the Reshetikhin-Turaev 3-manifold invariants coming from quantum groups in terms of R-matrices and such, what's the best reference to read?
Edit: Apparently I'm being too vague. Let me explain my motivation a little bit. Right now, I'm thinking about how to categorify Chern-Simons theory. I understand most of the maps from quantum groups like the R-matrix quite well, so I would like a good reference that has formulae I can try to categorify based the bits I already understand.