We present a simple regulator-type framework designed specifically for modeling formation of dwarf galaxies. Despite its simplicity, when coupled with realistic mass accretion histories from simulations and reasonable modeling choices the framework can reproduce a remarkably broad range of observed properties of dwarf galaxies over seven orders of magnitude in stellar mass down to the ultra-faint galaxies. In particular, we show that the model can simultaneously match observational constraints on the stellar mass-halo mass relation, as well as observed relations between stellar mass and gas phase and stellar metallicities, gas mass, size, and star formation rate, as well as general form and diversity of star formation histories (SFHs) of observed dwarf galaxies. We show that colors and surface brightness distributions of model galaxies are in good agreement with observed distributions for dwarfs in recent observational surveys. Furthermore, we show that the fraction of haloes that host detectable ultra faint galaxies is sensitive to the reionization redshift and this enables us to obtain constraints on the reionization redshift for the Local Group environment. Accounting for sub-halo disruption and observational detectability in current surveys, we forward model the satellite luminosity function and radial distributions using our model and show that they are in good agreement with observations. We also use this model to make predictions for satellite luminosity functions of Milky Way and M31 down to the faintest ultra-faint dwarfs.