There are two very important aspects to avoiding plagiarism in literature reviews.
The first is the most obvious one. That is, you need to be sure that you keep good track of what you have gotten from each of your sources. You need to have a way of marking these ideas in every draft of your review so that you do not forget that it is someone else's idea. This may sound obvious, but when you immerse yourself in your sources to the extent that you need to, you tend to forget what is yours and what isn't.
The second thing to do is what you might call a more holistic approach. You want to find a way to synthesize what you are reading rather than simply reporting what each source says. In other words, you want to read the literature and try to figure out basic differences between various groups of sources. You can then write something like "on one side of this debate are those who say that..." You then go on to list the major ideas that are common to this group. If there are small differences, you can mention them, being sure to cite sources for each. To see how this is done, be sure to read the literature review sections of other people's dissertations or other major academic works.
Many instances of plagiarism come due to ignorance of what constitutes a violation. My best advice to avoid plagiarism is threefold:
1. Always rewrite information in your own words- If you want to use a particular small quote make sure that it is in quotation marks but, otherwise, always rewrite the author's points using entirely different wording. If you are using 3 or more words in a row that are stated in the same way as the author, make sure to put that information in quotes. If you are unsure if you have violated this rule, submit your paper through a plagiarism checker.
2. Always use in-text citations if that is the way your school wants you to do citations. Any paragraph that you write that contains an idea that you developed based on reading another author's work (generally all but the introductory paragraph and the conclusion) should contain an in-text citation for the work that is paraphrased. For information on how to properly format in-text citations please review MLA or APA resources or whichever style guide you are using in your school.
3. Utilize all tools available to learn about what constitutes plagiarism. I really like: http://owl.english.purdue.edu/
4. And, do not copy and paste information from the Internet into your papers as if you were the author. If you are going to use a source from the Internet, please use proper citations, and put it in quotation marks. I periodically run my students' papers through the plagiarism checker and Google to see if the material has been copied verbatim from the Internet.
Hopefully this information helps.