NVDA typically requires the
MathCAT add-on to read math content. I'm not sure if that is the case when reading MathJax though. Can't test because I already have MathCAT installed.
There are some really simple navigation commands that will get you a long way. I tend to use the down arrow to move through everything, but this will hit everything on the page, which can be tedious. Using the Tab key will jump you to "clickable" objects, like links, buttons, and, with MathJax, math content. You can use H to move between headings on a page. If you add Shift to Tab or H, you'll move through those items in the opposite direction. That should be enough to get you around a document for basic testing.
You have to pay special attention to "focus" vs. "browse" mode when using NVDA. Basically, focus mode is for entering text, and browse mode is for navigation. You'll hear beeps from NVDA when moving between these modes. If you're trying to move through a page and the scroll bar starts moving instead of NVDA moving through the content, that means you've entered focus mode, and you need to toggle to browse mode. The command to switch between browse and focus mode is NVDA key + Spacebar. You can define your NVDA modifier key in the NVDA Preferences (Preferences > Settings > Keyboard).
Once NVDA has focus on math content, it should read aloud. If you want to explore the expression in greater detail, hit Enter on the expression. This will let you navigate the terms with greater control. Using the down arrow will "drill down" on the expression until you're investigating individual terms. Up arrow will "zoom out" until you're reading the entire expression at once. With whatever level you've drilled down to, you can use the right and left arrows to move through the expression in chunks. If this doesn't work for you right away, try right clicking on the expression (Shift + F10), then go to Accessibility > Activate. You may need to refresh the page after.
I think that should be all you really need to know to do some basic testing with NVDA in a document. I welcome any corrections on MathJax stuff I may have misinterpreted.
Michael Cantino