Gravitational light deflection due to mass along the line of sight will distort the images of background sources. Although an individual galaxy is not massive enough to cause a detectable lensing distortion in the background population, this effect can be measured statistically for a population of galaxies, and a first detection was claimed recently by Brainerd, Blandford, & Smail (BBS). BBS modeled their observations by describing galaxy halos as isothermal spheres of velocity dispersion σ, truncated at a radius s, where σ and s scale with the luminosity of the galaxy. Through Monte Carlo simulations they predicted the mean image polarization as a function of radius and compared it to the observations. In this paper we follow up on this discovery by developing a maximum-likelihood analysis that can constrain the halo properties of distant galaxy populations through galaxy-galaxy lensing; with it we show that the mean masses and sizes of halos can be estimated accurately, without excessive data requirements. The proposed maximum-likelihood analysis contains several important new elements: (1) it takes full account of the actual image ellipticities, positions, and apparent magnitudes, and as a consequence, it provides more efficient parameter estimation; (2) it provides automatically the proper relative weight for images of different ellipticities; (3) it uses a redshift probability distribution for each galaxy image and does not require a foreground lens-background image dichotomy; (4) it provides a rigorous means to investigate the covariances among the parameters that describe the halo model. We apply this analysis technique to simulated observations, using for ease of comparison the same lens model as BBS, and determine the best-fitting values, σ* and s*, corresponding to an L* galaxy. We explore two different observing strategies: (1) taking deep images (e.g., with HST) on small fields, and (2) using shallower images on larger fields. From these simulations we find that σ* can be determined to 10% accuracy if a sample of about 5000 galaxies with measured ellipticities are available, down to R 23. The corresponding data can be obtained on a 4 m class telescope in a few nights of very good seeing. Alternatively, the same accuracy in the determination of σ* can be achieved from about 10 moderately deep WFPC2 fields, on which galaxy shapes can be measured to about R ~ 25 and for which ground-based images are available on which the WFPC2 fields are centered. Firm lower limits can be set on the radial extent of the halo, but the maximal halo extent is poorly constrained. We show that this likelihood approach can also be used to constrain other parameters of the galaxy population, such as the Tully-Fisher index or the mean redshift of the galaxies as a function of apparent magnitude. Finally, we show how multicolor information, constraining the redshift of individual galaxies, can dramatically improve the accuracy of the parameter determination.