Accepted for publication in ApJ, 22 pages, 11 figures, 4 tables, the complete data tables can be found in the source ; The recent star formation (SF) in the early-type spiral galaxy M81 is characterized using imaging observations from the far-ultraviolet (UV) to the far-infrared (IR). We compare these data with models of the stellar, gas, and dust emission for sub-galactic regions. Our results suggest the existence of a diffuse dust emission not directly linked to the recent SF. We find a radial decrease of the dust temperature and dust mass density, and in the attenuation of the stellar light. The IR emission in M81 can be modeled with three components: 1) cold dust with a temperature =18+-2 K, concentrated near the HII regions but also presenting a diffuse distribution; 2) warm dust with T_w=53+-7 K, directly linked with the HII regions; and 3) aromatic molecules, with diffuse morphology peaking around the HII regions. We derive several relationships to obtain total IR luminosities from IR monochromatic fluxes, and we compare five different star formation rate (SFR) estimators for HII regions in M81 and M51: the UV, Halpha, and three estimators based on Spitzer data. We find that the Halpha luminosity absorbed by dust correlates tightly with the 24 microns emission. The correlation with the total IR luminosity is not as good. Important variations from galaxy to galaxy are found when estimating the total SFR with the 24 microns or the total IR emission alone. The most reliable estimations of the total SFRs are obtained by combining the Halpha emission (or the UV) and an IR luminosity (especially the 24 microns emission), which probe the unobscured and obscured SF, respectively. For the entire M81 galaxy, about 50% of the total SF is obscured by dust. The percentage of obscured SF ranges from 60% in the inner regions of the galaxy to 30% in the outer zones.