For the first time we show the detailed, late-stage, chemical evolution history of a small nearby dwarf spheroidal galaxy in the Local Group. We present the results of a high-resolution (R ~ 20 000, λ = 5340-5620; 6120-6701) FLAMES/GIRAFFE abundance study at ESO/VLT of 81 photometrically selected, red giant branch stars in the central 25' of the Fornax dwarf spheroidal galaxy. We also carried out a detailed comparison of the effects of recent developments in abundance analysis (e.g., spherical models vs. plane-parallel) and the automation that is required to efficiently deal with such large data sets. We present abundances of α-elements (Mg, Si, Ca, and Ti), iron-peak elements (Fe, Ni, and Cr), and heavy elements (Y, Ba, La, Nd, and Eu). Our sample was randomly selected and is clearly dominated by the younger and more metal-rich component of Fornax, which represents the major fraction of stars in the central region. This means that the majority of our stars are 1-4 Gyr old, and thus represent the end phase of chemical evolution in this system. Our sample of stars has unusually low [ α/Fe] , [Ni/Fe], and [Na/Fe] compared to the Milky Way stellar populations at the same [Fe/H]. The particularly important role of stellar winds from low-metallicity AGB stars in the creation of s-process elements is clearly seen from the high [Ba/Y]. Furthermore, we present evidence of an s-process origin of Eu. Based on FLAMES observations collected at the European Southern Observatory, proposal number 171.B-0588.Tables A1-A5 are only available in electronic form at http://www.aanda.org