Discourse analysis means different things to different people dependent on their philosphocal and theoretical background.
Basically discourse analysis means a way of approaching a problem or a situation through 'deconstructing' the text. That is getting to understand the hidden motivation behind the text. For example discourse analysis is quite often used to analyse political text to try and understand power relations.
Discourse analysis is not about trying to make a claim to a 'truth' or an absolute reality. It is more about providing an opportunity for debate to facilitate growth.
There is no one accepted way of undertaking research involving discourse analysis and even well known authors on the subject are open to ongoing criticism of their approach. However, this all provides further opportunty for debate and ultimately growth.