AIMS: Nova Cyg 2006 has been intensively observed throughout its full outburst. We investigate the energetics and evolution of the central source and of the expanding ejecta, their chemical abundances and ionization structure, and the formation of dust. METHOD: We recorded low, medium, and/or high-resolution spectra (calibrated into accurate absolute fluxes) on 39 nights, along with 2353 photometric UBVRcIc measures on 313 nights, and complemented them with IR data from the literature. RESULTS: The nova displayed initially the normal photometric and spectroscopic evolution of a fast nova of the FeII-type. Pre-maximum, principal, diffuse-enhanced, and Orion absorption systems developed in a normal way. After the initial outburst, the nova progressively slowed its fading pace until the decline reversed and a second maximum was reached (eight months later), accompanied by large spectroscopic changes. Following the rapid decline from second maximum, the nova finally entered the nebular phase and formed optically thin dust. We computed the amount of formed dust and performed a photo-ionization analysis of the emission-line spectrum during the nebular phase, which showed a strong enrichment of the ejecta in nitrogen and oxygen, and none in neon, in agreement with theoretical predictions for the estimated 1.0 Msun white dwarf in Nova Cyg 2006. The similarities with the poorly investigated V1493 Nova Aql 1999a are discussed. Comment: in press in Astronomy and Astrophysics