Every CDA study should consist in applying a given theory, model, method to a given dataset. In your case, if, for instance, you choose van Dijk's socio-cognitive framework, generally van Dijk proceeds by investigating choices at linguistic levels (lexis, syntax, semantics), combining them with the way the event in question is framed and the rhetorical choices made by the author. If you go to his earlier CDA publications, you will see how van Dijk conducts CDA in practice.

If you want to read about how other scholars apply CDA on specific areas of knowledge, you may want to go to the following link, which is a book review I wrote some 15 years ago (Review of An introduction to critical discourse analysis in education, edited by Rebecca Rogers. Mahwah, New Jersey: Lawrence Erlbaum Associates, 2004). Available online at http://linguistlist.org/pubs/reviews/get-review.cfm?SubID=47478

I hope this is helpful.

Check my article on inaugural address by Bush and Obama, available on reserachgate

Thanks a lot for your valuable advices Zouheir Maalej and Reza Biria