We present the design and methods of the COS-Halos survey, a systematic investigation of the gaseous halos of 44 z = 0.15-0.35 galaxies using background QSOs observed with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope. This survey has yielded 39 spectra of z_em ~ 0.5 QSOs with S/N ~ 10-15 per resolution element. The QSO sightlines pass within 150 physical kpc of the galaxies, which span early and late types over stellar mass log M* / Msun= 9.5 - 11.5. We find that the CGM exhibits strong HI, averaging 1 Ang in Lya equivalent width out to 150 kpc, with 100% covering fraction for star-forming galaxies and 75% covering for passive galaxies. We find good agreement in column densities between this survey and previous studies over similar range of impact parameter. There is weak evidence for a difference between early- and late-type galaxies in the strength and distribution of HI. Kinematics indicate that the detected material is bound to the host galaxy, such that >~90% of the detected column density is confined within +/-200 km s^-1 of the galaxies. This material generally exists well below the halo virial temperatures at T<~ 10^5 K. We evaluate a number of possible origin scenarios for the detected material, and in the end favor a simple model in which the bulk of the detected HI arises in a bound, cool, low-density photoionized diffuse medium that is generic to all L* galaxies and may harbor a total gaseous mass comparable to galactic stellar masses.
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