  We present total infrared (IR) and ultraviolet (UV) luminosity functions
derived from large representative samples of galaxies at z ~ 0, selected at IR
and UV wavelengths from the IRAS IIFSCz catalogue, and the GALEX AIS
respectively. We augment these with deep Spitzer and GALEX imaging of galaxies
in the 11 Mpc Local Volume Legacy Survey (LVL), allowing us to extend these
luminosity functions to lower luminosities (~10^6 L_sun), and providing good
constraints on the slope of the luminosity function at the extreme faint end
for the first time. Using conventional star formation prescriptions, we
generate from our data the SFR distribution function for the local Universe. We
find that it has a Schechter form, that the faint-end slope has a constant
value (to the limits of our data) of {\alpha} = -1.51 \pm 0.08, and the
'characteristic' SFR is 9.2 M_sun/yr. We also show the distribution function of
the SFR volume density; we then use this to calculate a value for the total SFR
volume density at z ~ 0 of 0.025 \pm 0.0016 M_sun/yr/Mpc^-3, of which ~ 20% is
occurring in starbursts. Decomposing the total star formation by infrared
luminosity, it can be seen that 9 \pm 1% is due to LIRGs, and 0.7 \pm 0.2% is
occuring in ULIRGs. By comparing UV and IR emission for galaxies in our sample,
we also calculate the fraction of star formation occurring in dust obscured
environments, and examine the distribution of dusty star formation: we find a
very shallow slope at the highly extincted end, which may be attributable to
line of sight orientation effects as well as conventional internal extinction.
