Discourse analysis can mean several things, ranging from Foucault to the British version of conversation analysis, so it would help if you clarified what your theoretical (and substantive) interests are.
I am trying to identify one's position regarding a phenomenon. I wonder why type of analysis is suitable to identify one's position using discourse analysis. Currently I am reading Harvey and Sacks notions on justifications and excuses. I wonder what type of analysis is suitable to complement Harvey and Sacks. I am also reading on Antaki's work.
If your interested in positioning, as a discursive process where selves are located in conversations and jointly produced story lines, there are a number. Depending on interactive positioning or reflexive positioning, but Davies & Harré - Positioning: The Discursive Production of Selves and works by Michael Bamberg, Anna De Fina, Arnulf Depperman, may be of interest.
Read Hermeneutics and Discourse Analysis in Social Psychology by S. Rettig & T. Hayes. {Publisher is Nova Science series. 2012. It provides theoretical material as well as actual analyses of discourses .
http://www.slideshare.net/tesono/content-analysis-and-discourse-analysis [content analysis and discourse analysis]
https://www.maxwell.syr.edu/uploadedFiles/moynihan/cqrm/Newsletter2.1.pdf [Symposium: Discourse and Content Analysis]
For my experiences, I am familiar with content analysis that can use for multi discipline (for me, i use it as my knowledge engineering method to getting information and making knowledge).