This thesis describes significant advances in experimental capabilities using ultracold polar molecules. While ultracold polar molecules are an idyllic platform for quantum chemistry and quantum many-body physics, molecular samples prior to this work failed to be quantum degenerate, were plagued by chemical reactions, and lacked any evidence of many-body physics. These limitations were overcome by loading molecules into an optical lattice to control and eliminate collisions and hence chemical reactions. This led to observations of many-body spin dynamics using rotational states as a pseudo-spin, and the realization of quantum magnetism with long-range interactions and strong many-body correlations.