Usually, you shouldn't cite lectures notes under MLA, APA, Chicago and Canadian style citations. However, depending on your course and prof, you can either add the phrase "lecture notes" to the citation or if the lecture notes are republications of books or articles, cite as if they were the books. Ask your prof on that one.

As for what qualifies as common knowledge, use your best judgment and cite when in doubt. A good rule of thumb is assume most things taught at the elementary and junior high school levels would fall under common knowledge.

Thanks and another question. I am covering Descartes' Meditations do I need to cite everything I get from it? If so, how do I abbreviate it?

Yes, you would need to cite everything you get from it just once (if you use a same idea or concept in two or more places in your paper, you only need to cite the first instance). For in-text citations, usually, (Descartes, page number) would do.

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Take a look at some cite websites:
APA: APA Style Guide
MLA: MLA citation style
The Rest: Citation and Style Guides

I am using the Chicago Style, but the guide I have does not have those answers. Thank you! That helped a lot!

Most lecture notes are generally paraphrases of lectures and border therefore on original work by the note taker; where exact phrases or sentences were transcribed, they can be cited as any public lecture would be.

Citations of Descartes are generally made using the pagination of the Adams & Tannery edition, and is shown in the margins of most scholarly translations. Your first citation should, though, also include the information of the translation you are using.

More often than not, citations serve two purposes: first, they allow a reader to verify the quotation, and second, to show its textual place in the philosopher's argumentation.

One can assume that the reader is acquainted with Cartesian terminology (e.g.,"the cogito", "thinking substance") so unless the precise term or phrase is important to your analysis or argument, it need not be footnoted.