Our understanding of the formation of planets hinges on the study of protoplanetary disks. These disks of dust and gas form alongside young stars, and are the birthplace of planetary systems. Critical to understand- ing the myriad physical mechanisms governing the formation of planets is the turbulence in protoplanetary disks, which has thus far remained difficult to measure. Observations using the Atacama Large Millimeter Array (ALMA) offer an unprecedented view into the physical environment surrounding stars and planets as they form. This thesis presents new methods for work- ing with ALMA observations to determine important disk parameters, particularly the turbulence and temperature profiles. New software is presented which provides a powerful new tool for modeling and fitting protoplanetary disk structure, which combines state of the art ray tracing with Markov Chain Monte Carlo techniques to offer a fast and scalable modeling and fitting framework. This software is used for several projects related to disk turbulence measurement. First, it is used to demonstrate how best to determine tem- perature in protoplanetary disks from optically thick molecular emission lines observed with ALMA. Techniques are presented to avoid potential problems which lead to incorrect measurement of brightness temperature due to inclusion of optically thin emission, and improperly applied contin- uum subtraction. Application of these techniques is shown for the specific case of HD 142527, a disk which has a significant asymmetric feature, whose temperature must be determined with care. The fitting and modeling framework is also used to determine the turbulence present in a set of inclined protoplanetary disks, HD 163296, DoAr 25, and HD 142666, by determining how the vertical dust structure of these disks has settled relative to the gas structure. The models are based on observations of these disks from the ALMA Disk Substructures at High Angular Resolution Project (DSHARP) project, which provided high angular and spectral resolution observations of the continuum, as well as CO rotational transitions. In two of the cases, HD 163296 and DoAr 25, the disk turbulence appears to be quite low, and in the case of HD 142666, we place an upper bound. These fits also provide detailed models of the structure of these disks, in both gas and dust, as well as higher accuracy than before in measurements of the stellar masses.