Try reading the pdf documentation that comes with Axe.  It explains a lot and has a mini tutorial/example program.

Hi and welcome to the forums!

First of all, make sure to know TI-BASIC very well prior learning Axe. Axe language looks slightly like BASIC syntax, so it will help a bit. A good journey towards http://tibasicdev.wikidot.com can help. Afterward, as people said, the Axe documentation and command index is a good read. Do not start too big. Try bits of code like a sprite moving around with nothing else, then collision with black pixels or getting used to pointers. It's best that you try reading those so you can understand easier, then if you do not understand something, feel free to check the forums for possible answers or ask here.