Philippe Flajolet and Robert Sedgewick's Analytic Combinatorics is the most comprehensive reference, available at http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html. Also useful is Odlyzko's "Asymptotic methods in enumeration" (from The Handbook of Combinatorics) at http://www.dtc.umn.edu/~odlyzko/doc/asymptotic.enum.pdf.