  We present and characterize the galaxy-galaxy lensing signal measured using
the first three years of data from the Dark Energy Survey (DES Y3) covering
4132 deg$^2$. These galaxy-galaxy measurements are used in the DES Y3
3$\times$2pt cosmological analysis, which combines weak lensing and galaxy
clustering information. We use two lens samples: a magnitude-limited sample and
the redMaGic sample, which span the redshift range $\sim 0.2-1$ with 10.7 M and
2.6 M galaxies respectively. For the source catalog, we use the Metacalibration
shape sample, consisting of $\simeq$100 M galaxies separated into 4 tomographic
bins. Our galaxy-galaxy lensing estimator is the mean tangential shear, for
which we obtain a total S/N of $\sim$148 for MagLim ($\sim$120 for redMaGic),
and $\sim$67 ($\sim$55) after applying the scale cuts of 6 Mpc/$h$. Thus we
reach percent-level statistical precision, which requires that our modeling and
systematic-error control be of comparable accuracy. The tangential shear model
used in the 3$\times$2pt cosmological analysis includes lens magnification, a
five-parameter intrinsic alignment model (TATT), marginalization over a
point-mass to remove information from small scales and a linear galaxy bias
model validated with higher-order terms. We explore the impact of these choices
on the tangential shear observable and study the significance of effects not
included in our model, such as reduced shear, source magnification and source
clustering. We also test the robustness of our measurements to various
observational and systematics effects, such as the impact of observing
conditions, lens-source clustering, random-point subtraction, scale-dependent
Metacalibration responses, PSF residuals, and B-modes.
