A large amount of physically useful information is contained in the vast data sets coming from single-molecule experiments. Numerical methods which estimate stochastic differential equations (SDEs) using observational data are presented. The information in these models can be used to approximate the dynamics, indirectly infer how structure influences kinetics, and quantitatively understand how noise from different time scales influences small scale systems relevant to targeted drug design using modern statistical analysis tools. Local maximum likelihood ideas are used throughout and the computational tools can also be used to quantitatively compare data-driven models to purely theoretical models to either refine existing and/or guide the development of new models. Results and insights provided by applying these methods to experimental single-stranded DNA and titin I27 time series data are presented.