A theoretical study of low-pressure helium rf glow-discharge plasmas is presented. The numerical scheme provides a fully kinetic description of the electrons and singly charged He ions in one spatial dimension and predicts the electric fields present in a mutually consistent fashion. The results have implications for a variety of discharge geometries and gases. Realistic, detailed cross sections for He are used. Both the numerical algorithm and physical processes are discussed. Unlike previous theoretical studies, we find a low average electron energy (< 1 eV) in the central bulk region and a weak bulk field (almost-equal-to 2 V/cm peak amplitude) that is out of phase with the strong sheath fields. The discussion emphasizes quantities that can be readily measured in order to facilitate comparison with experiment. Metastable-atom production rates are used as source terms in a diffusion-reaction model to predict metastable-atom densities. Multistep ionization due to metastable-atom-metastable-atom collisions is shown to be important for some of the conditions studied. The pressure dependence of the ion distribution at the electrode is studied. Some common approximations used in modeling discharges are examined for both suitability and possible improvement.