I recommend reading Natalia Knoblock 's work on discourses on Donald Trump's Facebook page. See especially "Xenophobic Trumpeters" (2017) and "Negotiating dominance on Facebook" (2020).
I would say critical discoursed analysis could be one way to go about it. But it also depends on what you are after. Van Dijk have a great website with publications on CDA. http://www.discourses.org/download/articles/