The best “first thing to read” about the Push programming language is the Push Redux. This presents Push’s core ideas in the context of recent versions of the language, with concrete examples.
Following that, you might want to check out the Push project page, the first journal article on Push (which describes an outdated version of the language, but provides an introduction to some of the goals of the Push project), and the Push3 conference paper (which introduced the exec stack, which is central to more recent versions of the language). You might also find these tutorial slides to be helpful: spector-tutorial-gecco2016.key.pdf (1.5 MB)