A literature review is very similar to a research paper in that it will be governed by a research question. Research questions help you narrow the focus of your topic and also help you analyze research on the topic. For example, your current topic "studies into the use of language games in teaching English vocabulary" is a bit broad. To narrow the topic and help you analyze it, you could ask the research question, "What are the pros and cons of using language games in teaching English vocabulary?" The question allows you to begin finding research on studies showing both the pros and cons concerning the topic. Then, as with a research paper, you will be summarizing and synthesizing your sources in an organized manner. When summarizing, you'll be explaining the main ideas of your sources in your own words. However, sometimes you may find that multiple sources discuss the same or similar main ideas, and that's when synthesizing your sources becomes useful. Rather than explaining each source separately, you can group them according to ideas you are trying to present, which we call synthesizing.
A major difference between a research paper and a literature review, however, is that for a literature review, you do not need to formulate your own argument. Instead, you'll simply be summarizing and synthesizing information. In the process, you may find that new interpretations of the information can be born and use your literature review to disclose this new interpretation. Alternatively, you might use your review to "trace the intellectual progression of the field, including major debates" (The University of North Carolina at Chapel Hill, The Writing Center, "Literature Reviews"). Still further, you might choose to use your review to "evaluate the sources and advice the reader on the most pertinent or relevant" ("Literature Reviews").
Once you've narrowed your focus by choosing a research question, you'll want to conduct your research by finding scholarly articles in peer reviewed journals; it's easiest to find such sources in your school's online library databases. Finding a useful keyword search is also important. For your particular research, you might try the search phrase "studies in language games in teaching English." For me, that keyword phrase yielded quite a few results that will probably be useful starting points for your research, including the article titled "Investigating the Impact of Using Games in Teaching Children English," by authors Ying-Jian Wang, Hui-Fang Shang, and Paul Biody, published in volume 1, issue 1 of the International Journal of Learning and Development, 2011. A second possibly useful article to begin your research is titled "The Effect of Games on Learning Vocabulary," by authors Maryam Rohani and Behzad Pourgharib, published in volume 4 of the International Research Journal of Applied and Basic Sciences, 2013.