  We present new Very Large Array observations at five frequencies, from 1.4 to
22GHz, of the extremely low-metallicity blue compact dwarf SBS0335-052. The
radio spectrum shows considerable absorption at 1.49GHz, and a composite
thermal+non-thermal slope. After fitting the data with a variety of models, we
find the best-fitting geometry to be one with free-free absorption
homogeneously intermixed with the emission of both thermal and non-thermal
components. The best-fitting model gives an an emission measure EM ~ 8x10^7pc
cm^{-6} and a diameter of the radio-emitting region D ~17pc. The inferred
density is n_e ~ 2000 cm^{-3}. The thermal emission comes from an ensemble of
\~9000 O7 stars, with a massive star-formation rate (>=5Msun) of 0.13-0.15
yr^{-1}, and a supernova rate of 0.006 yr^{-1}. We find evidence for ionized
gas emission from stellar winds, since the observed Bralpha line flux
significantly exceeds that inferred from the thermal radio emission. The
non-thermal fraction at 5GHz is ~0.7, corresponding to a non-thermal luminosity
of ~2x10^{20} W Hz^{-1}. We attribute the non-thermal radio emission to an
ensemble of compact SN remnants expanding in a dense interstellar medium, and
derive an equipartition magnetic field of ~0.6-1 mG, and a pressure of
\~3x10^{-8}-1x10^{-7} dyne cm^{-2}. If the radio properties of SBS0335-052 are
representative of star formation in extremely low-metallicity environments,
derivations of the star formation rate from the radio continuum in high
redshift primordial galaxies need to be reconsidered. Moreover, photometric
redshifts inferred from ``standard'' spectral energy distributions could be
incorrect.
