In a literature review, we look at recent publications and put what other researchers have said in this context. However, how can I develop my own argument? Should I write it with my own words or should the argument be based in what others have said?
Damien Igoe's answer is very accurate, however, I would add that I think it is possible to interpret what someone wrote in a different way than others have previously interpreted. However, your arguments should not be confused with the other authors' arguments.
Originality in analysis is often welcomed. However, originality in structure should be done very carefully. Common structures exist for a reason. In my field, it is common to switch between the reviewed author's points and your own:
Jones (1991) claimed that the primary motivator for workers was public recognition while Smith (2004) believed that workers were more concerned with monetary compensation. I will show that both were correct by showing that workers really care most about their compensation being publicly higher than the average for their position.
The literature review is just that, a review of the published literature - synthesised and analysed. Developing your own arguments should occur after this review as you then have something to refer back to when developing your stance.
A study technique I use, is as I am reviewing the literature for this chapter, I keep a notepad near by and jot down parts of my argument as I proceed.
I would offer a slightly different answer from either of the others, both of which are excellent. Each of these answers and my own are probably (at least somewhat) discipline-specific.
Rarely, in my view, should a literature review be just that - a simple review. Instead, the best structure for papers in my field is an introduction, followed by a single section that provides theory and specific hypotheses derived from that theory, followed by empirics, etc. There is no "literature review" per se.
Instead, literature that is relevant for establishing a problem is cited in the introduction and literature relevant for building new theory, elaborating existing theory, and/or challenging existing evidence/arguments is cited in the course of making one's theoretical argument. From that argument come testable hypotheses, all of this being stated in one section (possibly with subsections, depending on the scope of the paper) between introduction and research design.
In this way, relevant literature is reviewed in the course of constructing arguments, with quotes and references both bringing credibility to your arguments and being used to demonstrate weaknesses in extant work. Thus, your review should be your own argument largely in your own words, with others' work cited and sparingly quoted where it helps you.