Webpages expire, books and articles get lost, photographs and films degrade. Citations are necessary to assure that the next researcher can find the same information through different means.
Citing is important for your scholarly credibility, and for building on previous research. You may have a good idea, but simply stating it does not make it true or believable. Give your ideas validity and support by citing established authors.
Avoiding plagiarism is key to academic honesty. Claiming someone's original work as your own is fraud. Citations give authors their due credit.
The Online Writing Lab at Purdue University has instructions and examples on APA and MLA citation styles.
The Excelsior College Online Writing Lab provides extensive information on the writing process, evaluating research, and tutorials on building citations in APA, MLA, and Chicago style(s).
The American Psychological Association has a great website of style examples and grammar guidelines. See the References section for basic principles of reference lists, examples of references, DOIs, and more.
The Modern Language Association's MLA Style Center provides advice and examples.
And, if you're looking for authoritative examples of Chicago style of notes and bibliography, check the Chicago Manual of Style quick citation guide.