A good book in algebraic combinatorics that describes the research process is David M. Bressoud's "Proofs and Confirmations". From the back cover:
This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author tells the story of the search for and discovery of a proof of a formula conjectured in the early 1980s: the number of $n\times n$ alternating sign matrices, objects that generalize permutation matrices. Although it was soon apparent that the conjecture must be true, the proof was elusive....
