First, check with your professor to be sure which citation style is required (it's probably in the course syllabus).
Keep track of your sources as you gather information in case you need to track down the sources later when you start writing your paper.
Once you put together a few citations, you'll realize how easy it is. Whether it's MLA, APA or another citation style, you need the same basic information about each source you use. Learn to identify those bits of information and follow the guides for instructions on how to organize the information.
Many research databases like EbschoHost, Opposing Viewpoints, Gale Virtual Reference Library automatically generate citations for you when you click on a journal or article in an online book within that database. Look for a "CITE THIS" button or something simliar in each database. Copy and paste the citation to your tracking document. Usually you will only have to tweak the formatting - but you should always verify a citation generated from a database with the published MLA and APA guides.
Who cares about citing sources? Everyone!
You need to acknowledge your sources of information, whether you are quoting directly, paraphrasing, or summarizing someone's words.
It's not so much about your English professor making sure you reference your sources properly, your reader might want to actually track down the sources you used to read the full article. Researchers tend to follow leads provided by other researchers.
Here's how I might cite a movie review:
Roger Ebert basically gives the movie Argo a thumbs up ("Argo").
or, I could say:
The movie Argo was reviewed favorably by the notable critic from the Chicago Sun-Times (Ebert).
Either way, I'm going to look in my bibliography for something authored by Ebert, and here's how the work I cited would appear:
Ebert, Roger. "Argo." rogerebert.com. Chicago Sun-Times, 10 Oct. 2012. Web. 31 Mar. 2013.
Don't worry about page numbers in web sites, but do include the author and/or title of the work.
Note the abbreviation for the month of March in the above example. Follow common conventions for abbreviations in works cited.