We present new infrared observations of the central regions of the starburst galaxy M 82 . The observations consist of near-infrared integral field spectroscopy in the H - and K -band obtained with the MPE 3D instrument , and of \lambda = 2.4 - 45 ~ { } \mu m spectroscopy from the Short Wavelength Spectrometer ( SWS ) on board the Infrared Space Observatory . These measurements are used , together with data from the literature , to ( 1 ) re-examine the controversial issue of extinction , ( 2 ) determine the physical conditions of the interstellar medium ( ISM ) within the star-forming regions , and ( 3 ) characterize the composition of the stellar populations . Our results provide a set of constraints for detailed starburst modeling which we present in a companion paper . We find that purely foreground extinction can not reproduce the global relative intensities of H recombination lines from optical to radio wavelengths . A good fit is provided by a homogeneous mixture of dust and sources , and with a visual extinction of A _ { V } = 52 ~ { } { mag } . The SWS data provide evidence for deviations from commonly assumed extinction laws between 3 \mu m and 10 \mu m. The fine-structure lines of Ne , Ar , and S detected with SWS imply an electron density of \approx~ { } 300 ~ { } { cm ^ { -3 } } , and abundance ratios Ne/H and Ar/H nearly solar and S/H about one-fourth solar . The excitation of the ionized gas indicates an average effective temperature for the OB stars of 37400 K , with little spatial variation across the starburst regions . We find that a random distribution of closely packed gas clouds and ionizing clusters , and an ionization parameter of \approx 10 ^ { -2.3 } represent well the star-forming regions on spatial scales ranging from a few tens to a few hundreds of parsecs . From detailed population synthesis and the mass-to- K -light ratio , we conclude that the near-infrared continuum emission across the starburst regions is dominated by red supergiants with average effective temperatures ranging from 3600 K to 4500 K , and roughly solar metallicity . Our data rule out significant contributions from older , metal-rich giants in the central few tens of parsecs of M 82 .