We have carried out quantitative observations of the vector magnetic field during the emergence of three small bipolar active regions in June, 1992, July 1993, and September 1994 using the Advanced Stokes Polarimeter (ASP). The region of horizontal magnetic field at the actual site of emergence is always characterized by low magnetic field strength (i.e. considerably less than 1000 Gauss). We find a strong relationship between field strength and inclination in these regions. This suggests that 1) flux emerging from below the photosphere does not coalesce into strong flux tubes until it reaches the photosphere, becomes nearly vertical as a result of magnetic buoyancy, and is then acted upon by convective collapse, and 2) the field strength of flux rising through the convection zone may be in rough equipartition with the fluid motions. We find the flux emergence zone to be characterized by highly variable (both spatially and temporally) fill factors for the magnetic field, suggesting that the flux below the surface is filamentary, that it rises rapidly through the photosphere to form a magnetic canopy above the emergence region. Sequences of Hα on- and off-band images obtained with the ASP reveal the accompanying development of the arch-filament system, and suggest that the material within the Hα structures is supplied by a siphon flow as evidenced by apparent chromospheric red shifts on the sides of the loops closest to a large pore, and blue shifts where the fields anchor in plage regions. Proper motions of the magnetic flux images throughout a day's observation indicate the presence of a persistent vortex flow on a small scale (a few arcseconds). The National Center for Atmospheric Research is sponsored by the National Science Foundation.