  We compute the form factors for the $B \to Kl^+l^-$ semileptonic decay
process in lattice QCD using gauge-field ensembles with 2+1 flavors of sea
quark, generated by the MILC Collaboration. The ensembles span lattice spacings
from 0.12 to 0.045 fm and have multiple sea-quark masses to help control the
chiral extrapolation. The asqtad improved staggered action is used for the
light valence and sea quarks, and the clover action with the Fermilab
interpretation is used for the heavy $b$ quark. We present results for the form
factors $f_+(q^2)$, $f_0(q^2)$, and $f_T(q^2)$, where $q^2$ is the momentum
transfer, together with a comprehensive examination of systematic errors.
Lattice QCD determines the form factors for a limited range of $q^2$, and we
use the model-independent $z$ expansion to cover the whole kinematically
allowed range. We present our final form-factor results as coefficients of the
$z$ expansion and the correlations between them, where the errors on the
coefficients include statistical and all systematic uncertainties. We use this
complete description of the form factors to test QCD predictions of the form
factors at high and low $q^2$. We also compare a Standard-Model calculation of
the branching ratio for $B \to Kl^+l^-$ with experimental data.
