Context: We present observations of the GRB 080319B afterglow at optical, mm, and radio frequencies between a few hours and 67 days after the burst. Aims: We attempt to understand the nature of this extraordinarily bright explosion based on the observed properties and its comparison with afterglow models. Methods: Our observations and other published multiwavelength data were used to reconstruct the light curves and spectral energy distributions of the burst afterglow. Results: Our results indicate that the observed features of the afterglow agrees equally well with the inter stellar matter and the stellar wind density profiles of the circumburst medium. In the case of both density profiles, the maximum synchrotron frequency νm is below optical value and the cooling break frequency νc is below X-rays, ~104 s after the burst. The derived value of the Lorentz factor at the time of naked-eye brightness is also ~300 for a corresponding blast-wave size of ~1018 cm. Conclusions: The numerical fit to the multiwavelength afterglow data constraints the values of physical parameters and the emission mechanism of the burst. Based on observations obtained with the 0.22 m telescope at Russia the 0.7 m telescope at of Kharkov University, Ukraine, the 0.8 m telescope at Observatorio del Teide (IAC-80), Spain the 1.2 m Mercator telescope at La Palma, Spain, the 1.5 m telescope of Maidanak observatory Uzbekistan, the 2.0 m IGO Telescope at IUCAA Pune, India, the 2.5 m NOT, the PdB millimeter interferometric array France, the RATAN-600 Radio Telescope at Russia and the RT-22 radio telescope of CrAO, Ukraine.