By considering thermodynamics (phase diagrams) and some kinetics it is possible to gain an understanding of how a microstructure comes about. Phase diagrams are very powerful tools in interpreting micrographs, but there also exist many microstructures that can only be explained by considering things like diffusion limitation.
Porter, D. A. and Easterling K, Phase Transformations in Metals and Alloys, 2nd edition, Routledge, 1992.
G.A. Chadwick, Metallography of phase transformations, Butterworth & Co (Publishers) Ltd, 1972.
More information about TTT diagrams can be found on the MATTER website, see Transformation diagrams.