As data science and machine learning methods are taking on an increasingly important role in the materials research community, there is a need for the development of machine learning software tools that are easy to use (even for nonexperts with no programming ability), provide flexible access to the most important algorithms, and codify best practices of machine learning model development and evaluation. Here, we introduce the Materials Simulation Toolkit for Machine Learning (MAST-ML), an open source Python-based software package designed to broaden and accelerate the use of machine learning in materials science research. MAST-ML provides predefined routines for many input setup, model fitting, and post-analysis tasks, as well as a simple structure for executing a multi-step machine learning model workflow. In this paper, we describe how MAST-ML is used to streamline and accelerate the execution of machine learning problems. We walk through how to acquire and run MAST-ML, demonstrate how to execute different components of a supervised machine learning workflow via a customized input file, and showcase a number of features and analyses conducted automatically during a MAST-ML run. Further, we demonstrate the utility of MAST-ML by showcasing examples of recent materials informatics studies which used MAST-ML to formulate and evaluate various machine learning models for an array of materials applications. Finally, we lay out a vision of how MAST-ML, together with complementary software packages and emerging cyberinfrastructure, can advance the rapidly growing field of materials informatics, with a focus on producing machine learning models easily, reproducibly, and in a manner that facilitates model evolution and improvement in the future.