The star formation histories of four fields within the Local Group dwarf irregular galaxy NGC 6822 are presented. Each of the fields was imaged by the WFPC2 aboard the {it Hubble Space Telescope} and were used to obtain $VI$ color-magnitude diagrams for each field reaching $Vsimeq26$. The magnitude of the tip of the red giant branch and the red clump were used to determine distances to NGC 6822 that are consistent with previous ground-based measurements. The distance, extinction and star formation history were also determined by fitting the entire color-magnitude diagram in each field. The distances from these fits are consistent with the other determinations within the estimated errors once the systematic effects of uncertainties in the age-metallicity relation are taken into account. The extinction varies among the four fields from approximately the foreground Galactic value to $approx 0.4$ mag higher in $V$ and roughly correlates with the $60micron$ surface brightness. The star formation histories in the four fields are similar for ages $gtrsim 1$ Gyr and are relatively constant or somewhat increasing with time. These old star formation rates are comparable to that expected from the typical gas surface densities at these galactocentric radii and suggest that no large scale redistribution of gas or stars is required to account for the inferred star formation rates. Three of the fields show a drop of a factor of $sim 2-4$ in the star formation rate about 600 Myr ago while the remaining field centered on the bar shows an increase.
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