APA style, the stardard of American Psychological Association, is usually used in social and natural sciences, like psychology, linguistics, etc. MLA style, the stardard of Modern Language Association of America, is in the writings of humanities or liberal arts like literature, language, philosophy, etc. Outlines and basic examples of the two styles are shown in A Guide to MLA Documentation: With an Appendix on APA Style, written by Joseph F. Trimmer.
Modern Language Association, however, made a major change of its style in 1982. In Japan, on the other hand, many scholars of English literature have been using the old MLA style, which is still the stardard here. If your instructor wants you to write in MLA style, you'd better see whether it is the old or the new one. You can see examples of APA format and MLA formats, new and old, in Undergraduate Writing Center, University of Texas at Austin at "http://homer.cc.utexas.edu/depts/uwc/.html/citation.html".
You can also see examples of MLA format in Purdue University On-Line Writing Lab at "http://owl.english.purdue.edu/Files/33.html". Ursinus College, Pennsylvania, has many examples of MLA documentation at "http://www.ursinus.edu/myrin/mlastyle_index.html".
If you want detailed information on APA style, see Publication Manual of the American Psychological Association published by APA.
If you want detailed information on MLA style, see MLA Handbook for Writers of Research Papers by Joseph Gibaldi.