Most arguments you’ll deal with — outside of a logic textbook — will not be nicely formatted into clearly marked premises and conclusions. In normal writing and dialogue, premises are not always presented in the most logical order, some premises are implied and not stated at all, and some are lumped together in such a way that two or three premises are expounded in one sentence. There are, however, a number of contextual clues that can help you extract and reconstruct the argument in these cases.
There are certain keywords, or textual indicators, that will help you identify some of the premises and conclusions in an argument. Words and phrases such as: since, for, because, given that, subsequently, inasmuch as, etc. are textual indicators of a premise. Words like: therefore, hence, consequently, it follows, accordingly, etc. can be good indicators of a conclusion. While these words are not always used in this fashion, they are a good place to start when attempting to extract an argument from normal speech.
In long arguments containing multiple/nested sub-arguments, go through the piece carefully, and starting with the keyword method, highlight all the statements that appear to be premises and conclusions. Once that is done, map them out in either an outline or a diagram in order to analyse the argument.
Be generous: most arguments will have implied or missing premises. Add the necessary premises you know the author intended, even if she didn’t explicitly state them.