We have re-evaluated empirical expressions for the abundance determination of N, O, Ne, S, Cl, Ar and Fe taking into account the latest atomic data and constructing an appropriate grid of photoionization models with state-of-the art model atmospheres. Using these expressions we have derived heavy element abundances in the ~310 emission-line galaxies from the Data Release 3 of the Sloan Digital Sky Survey (SDSS) with an observed Hbeta flux F(Hbeta) > 10^-14 erg s^-1 cm^-2 and for which the [O iii] lambda4363 emission line was detected at least at a 2sigma level, allowing abundance determination by direct methods. The oxygen abundance 12 + log O/H of the SDSS galaxies lies in the range from ~7.1 (Z_&sun;/30) to ~8.5 (0.7 Z_&sun;). The SDSS sample is merged with a sample of 109 blue compact dwarf (BCD) galaxies with high quality spectra, which contains extremely low-metallicity objects. We use the merged sample to study the abundance patterns of low-metallicity emission-line galaxies. We find that extremely metal-poor galaxies (12 + log O/H < 7.6, i.e. Z < Z_&sun;/12) are rare in the SDSS sample. The alpha element-to-oxygen abundance ratios do not show any significant trends with oxygen abundance, in agreement with previous studies, except for a slight increase of Ne/O with increasing metallicity, which we interpret as due to a moderate depletion of O onto grains in the most metal-rich galaxies. The Fe/O abundance ratio is smaller than the solar value, by up to 1 dex at the high metallicity end. We also find that Fe/O increases with decreasing Hbeta equivalent width EW(Hbeta). We interpret this as a sign of strong depletion onto dust grains, and gradual destruction of those grains on a time scale of a few Myr. All the galaxies are found to have log N/O > -1.6, implying that they have a different nature than the subsample of high-redshift damped Lyalpha systems with log N/O of ~-2.3 and that their ages are larger than 100-300 Myr. We confirm the apparent increase in N/O with decreasing EW(Hbeta), already shown in previous studies, and explain it as the signature of gradual nitrogen ejection by massive stars from the most recent starburst.