First thing: Download the latest version of Max, if you haven't already.
If you want to dig in, here's a more detailed guide about our Tutorials and Reference Pages.

Navigate to Help > Browse Lessons to launch step-by-step patch-alongs with easy to follow videos.

Help > Reference will open up the Documentation browser where you can find tutorials and guides for more detailed explanations.

Or, navigate to Help > Examples to take a look at fully functional patches. Edit any patch, or take them apart to make them your own. Copy and paste from any patch into yours.
When in doubt, Max 8 features a powerful Search Sidebar to help you access thousands of resources in Max and online.
Find it by clicking on the search icon found at the top right hand side of the patcher window.

Instructables: Intro to MaxMSP
Youtube Series: Max 8 Tutorials
20 Objects: A Pragmatic Method for Learning Max/MSP/Jitter and Max for Live
Kadenze Online Course: "Programming Max: Structuring Interactive Software for Digital Arts"