We present a method which delivers a continuous, high-density beam of slow and internally cold polar molecules. In our source, warm molecules are first cooled by collisions with a cryogenic helium buffer gas. Cold molecules are then extracted by means of an electrostatic quadrupole guide. For ND3 the source produces fluxes up to (7±47)×1010molecules/s with peak densities up to (1.0±0.61.0)×109molecules/cm3. For H2CO the population of rovibrational states is monitored by depletion spectroscopy, resulting in single-state populations up to (82±10)%.