Ultracold molecules provide an exciting testing ground for studies of fundamental interactions, new states of matter, and metrology. Diatomic molecules based on two-electron atoms are especially suitable for precise tests of interatomic interactions, molecular quantum electrodynamics, electron-proton mass ratio variations, and other measurements in molecular and fundamental physics. This thesis describes the construction of a new strontium apparatus, from initial vacuum system setup through characterization of ultracold atom samples, followed by a new method of efficient, all-optical production of ultracold ^{88}Sr_2 molecules in an optical lattice, with detection via optical fragmentation. High-Q spectra of the weakly bound molecules in magnetic fields are studied, yielding precise binding energies, anomalously large molecular g factors resulting from large nonadiabatic effects, and strongly enhanced magnetic susceptibility. The thesis then concludes with an outlook on future experiments in our lab, including studies of forbidden molecular transitions, and longer term studies of fundamental physics from deeply bound Sr_2.