Aims: Fossil record methods based on spectral synthesis techniques have matured during the past decade, and their application to integrated galaxy spectra has fostered substantial advances in the understanding of galaxies and their evolution. Yet, because of the lack of spatial resolution, these studies are limited to a global view, providing no information about the internal physics of galaxies. Methods: Motivated by the CALIFA survey, which is gathering integral field spectroscopy (IFS) over the full optical extent of 600 galaxies, we have developed an end-to-end pipeline that: (i) partitions the observed datacube into Voronoi zones in order to, when necessary and taking due account of correlated errors, increase the signal-to-noise ratio; (ii) extracts rest-framed spectra, including propagated errors and bad-pixel flags; (iii) feeds the spectra into the starlight spectral synthesis code; (iv) packs the results for all galaxy zones into a single FITS or HDF5 file; (v) performs a series of post-processing operations, including zone-to-pixel image reconstruction and unpacking the spectral and stellar population properties derived by starlight into multidimensional time, metallicity, and spatial coordinates. This paper provides an illustrated description of the whole pipeline and its many products. Using data for the nearby spiral NGC 2916 as a showcase, we go through each of the steps involved and present a series of ways of visualizing and analyzing this manifold. These include 2D maps of properties such as the velocity field, stellar extinction, mean ages and metallicities, mass surface densities, and star formation rates on different time scales and normalized in different ways, as well as 1D averages in the temporal and spatial dimensions, which lead to evolutionary curves and radial profiles of physical properties. Projections of the stellar light and mass growth onto radius-age diagrams are introduced as a means of visualizing galaxy evolution in time and space simultaneously, something which can also be achieved in 3D with snapshot cuts through the (x,y,t) cubes. Results: The results vividly illustrate the richness both of the combination of IFS data with spectral synthesis and of the insights on galaxy physics provided by the variety of diagnostics and semi-empirical constraints obtained. Additionally, they give a glimpse of what is to come from CALIFA and future IFS surveys.