Quantum Monte Carlo calculations of nuclei with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mo>&lt;~</mml:mo><mml:mn>7</mml:mn></mml:math>

We report quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with $A&lt;~7$ using a realistic Hamiltonian containing the Argonne ${v}_{18}$ two-nucleon and Urbana IX three-nucleon potentials. A detailed description of the Green's-function Monte Carlo algorithm for systems with state-dependent potentials is given and a number of tests of its convergence and accuracy are performed. We find that the Hamiltonian being used results in ground states of both ${}^{6}$Li and ${}^{7}$Li that are stable against breakup into subclusters, but somewhat underbound compared to experiment. We also have results for ${}^{6}$He, ${}^{7}$He, and their isobaric analogs. The known excitation spectra of all these nuclei are reproduced reasonably well and we predict a number of excited states in ${}^{6}$He and ${}^{7}$He. We also present spin-polarized one-body and several different two-body density distributions. These are the first microscopic calculations that directly produce nuclear shell structure from realistic interactions that fit $\mathrm{NN}$ scattering data.