One important frontier for astronomical adaptive optics (AO) involves methods such as multi-object AO and multi-conjugate AO that have the potential to give a significantly larger field of view than conventional AO techniques. A second key emphasis over the next decade will be to push astronomical AO to visible wavelengths. We have conducted the first laboratory simulations of wide-field, laser guide star AO at visible wavelengths on a 10 m class telescope. These experiments, utilizing the UCO/Lick Observatory's multi-object/laser tomographic adaptive optics (MOAO/LTAO) test bed, demonstrate new techniques in wave front sensing and control that are crucial to future on-sky MOAO systems. We (1) test and confirm the feasibility of highly accurate atmospheric tomography with laser guide stars, (2) demonstrate key innovations allowing open-loop operation of Shack-Hartmann wave front sensors (with errors of ~30 nm) as will be needed for MOAO, and (3) build a complete error budget model describing system performance. The AO system maintains a performance of 32.4% Strehl ratio on-axis, with 24.5% and 22.6% at 10'' and 15'', respectively, at a science wavelength of 710 nm (R-band) over the equivalent of 0.8 s of simulation. The mean ensquared energy on-axis in a 50 mas spaxel is 46%. The off-axis Strehl ratios are obtained at radial separations 2-3 times the isoplanatic angle of the atmosphere at 710 nm. The MOAO-corrected field of view is ~25 times larger in area than that limited by anisoplanatism at R-band. The error budget we assemble is composed almost entirely of terms verified through independent, empirical experiments, with minimal parameterization of theoretical models. We find that error terms arising from calibration inaccuracies and optical drift are comparable in magnitude to traditional terms like fitting error and tomographic error. This makes a strong case for implementing additional calibration facilities in future AO systems, including accelerometers on powered optics, three-dimensional turbulators, telescopes, and laser guide star simulators, and external calibration ports for deformable mirrors. These laboratory demonstrations add strong credibility to the implementation of on-sky demonstrators of laser tomographic adaptive optics (LTAO) on 5-10 m telescopes in the coming years.