The first two tutorials are excellent for new users, and can be assigned to students as homework to learn Mathematica outside of class time.
Follow along in Mathematica as you watch this multi-part screencast that teaches you the basics—how to create your first notebook, calculations, visualizations, interactive examples, and more.
Provides examples to help you get started with new functionality in Mathematica 10, including machine learning, computational geometry, geographic computation, and device connectivity.
Access step-by-step instructions ranging from how to create animations to basic syntax information.
Search Wolfram's large collection of materials for example calculations or tutorials in your field of interest.