We present a study of semileptonic ($) over bar B --> Dl ($) over bar v decays in quenched lattice QCD through a calculation of the matrix element [D\($) over bar c gamma(mu)b\($) over bar B] on a 24(3) x 48 lattice at beta = 6.2, using an O(alpha)-improved fermion action. We perform the calculation for several values of the initial and final heavy-quark masses around the charm mass, and three values of the light-(anti)quark mass around the strange mass. Because the charm quark has a bare mass which is almost 1/3 the inverse lattice spacing, we study the ensuing mass-dependent discretization errors, and propose a procedure for subtracting at least some of them nonperturbatively. We extract the form factors h(+) and h(-). After radiation corrections, we find that h(+) displays no dependence on the heavy-quark mass, enabling us to identify it with an Isgur-Wise function xi. Interpolating the light-quack mass to that of the strange, we obtain an Isgur-Wise function relevant for ($) over bar B-s --> D-s*l ($) over bar v decays which has a slope -xi(s)' = 1.2(-2)(+2)(stat)(-1)(+2)(syst) at zero recoil. An extrapolation to a massless light quark enables us to obtain an Isgur-Wise function relevant for ($) over bar B --> D(*)l ($) over bar v decays. This function has a slope -xi(u,d)' = 0.9(-3)(+2)(stat)(-2)(+4)(syst) at zero recoil. We observe a slight decrease in the magnitude of the central value of the slope as the mass of the light quark is reduced; given the errors, however, the significance of this observation is limited. We then use these functions, in conjunction with heavy-quark effective theory, to extract V-cb with no free parameters from the ($) over bar B --> D*l ($) over bar v decay rate measured by the ALEPH, ARGUS, and CLEO Collaborations. Using the CLEO data, for instance, we obtain \V-cb\ = 0.037(-1-2-1)(+1+2+4)(0.99/1 + beta(A1)(1))1/1 + delta(1/mc2) where delta(1/mc2) is the power corrections inversely proportional to the square of the charm quark mass, and beta(A1)(1) is the relevant radiative correction at zero recoil. Here, the first set of errors is experimental, the second represents the statistical error, and the third represents the systematic error in our evaluation of the Isgur-Wise function. We also use our Isgur-Wise functions and heavy-quark effective theory to calculate branching ratios for ($) over bar B-(s) --> D-(s)l ($) over bar v and ($) over bar B-(s) --> D-(s)*l ($) over bar v decays.