  This is the first in a series of three papers describing a project with the
Cosmic Origins Spectrograph on the Hubble Space Telescope to measure abundances
of the neutral interstellar medium (ISM) in a sample of 9 nearby star-forming
galaxies. The goal is to assess the (in)homogeneities of the multiphase ISM in
galaxies where the bulk of metals can be hidden in the neutral phase, yet the
metallicity is inferred from the ionized gas in the HII regions. The sample,
spanning a wide range in physical properties, is to date the best suited to
investigate the metallicity behavior of the neutral gas at redshift z=0. ISM
absorption lines were detected against the far-ultraviolet spectra of the
brightest star-forming region(s) within each galaxy. Here we report on the
observations, data reduction, and analysis of these spectra. Column densities
were measured by a multi-component line-profile fitting technique, and
neutral-gas abundances were obtained for a wide range of elements. Several
caveats were considered including line saturation, ionization corrections, and
dust depletion. Ionization effects were quantified with `ad-hoc' CLOUDY models
reproducing the complex photoionization structure of the ionized and neutral
gas surrounding the UV-bright sources. An `average spectrum of a redshift z=0
star-forming galaxy' was obtained from the average column densities of
unsaturated profiles of neutral-gas species. This template can be used as a
powerful tool for studies of the neutral ISM at both low and high redshift.
