We derive relations between the Lyα surface brightness, star formation rate, and abundance of dust in damped Lyα absorption systems. These are idealized as plane-parallel objects in which the sources of Lyα photons are either distributed throughout the gas or confined to a thin, central sheet. For the dust-to-gas ratio in the damped Lyα systems, we adopt the typical value inferred from the reddening of background quasars. We then use the results of several recent searches for Lyα emission to set limits on, and in one case, estimate the star formation rate per unit area of the damped Lyα systems.