We present results from a detailed spectrophotometric analysis of the blue compact dwarf galaxy Mrk 35 (Haro 3), based on deep optical (B,V,R,I) and near-IR (J,H,K) imaging, Halpha narrow-band observations and long-slit spectroscopy. The optical emission of the galaxy is dominated by a central young starburst, with a bar-like shape, while an underlying component of stars, with elliptical isophotes and red colors, extends more than 4 kpc from the galaxy center. High resolution Halpha and color maps allow us to identify the star-forming regions, to spatially discriminate them from the older stars, and to recognize several dust patches. We derive colors and Halpha parameters for all the identified star-forming knots. Observables derived for each knot are corrected for the contribution of the underlying older stellar population, the contribution by emission lines, and from interstellar extinction, and compared with evolutionary synthesis models. We find that the contributions of these three factors are by no means negligible and that they significantly vary across the galaxy. Therefore, careful quantification and subtraction of emission lines, galaxy host contribution, and interstellar reddening at every galaxy position, are essential to derive the properties of the young stars in BCDs. We find that we can reproduce the colors of all the knots with an instantaneous burst of star formation and the Salpeter initial mass function with an upper mass limit of 100 M_solar. In all cases the knots are just a few Myr old. The underlying population of stars has colors consistent with being several Gyr old. Comment: 21 pages, 13 figures. Accepted for publication in ApJ, tentatively scheduled for the ApJ November 1, 2007 v669n1 issue