Here are some tips to make the process easier and more effective.
What is the structure of the article?
But the problem is that even "critical" morality can be wrong. The historyof moral philosophy is filled with quite analytical/critical theories anddiscussions that nevertheless turned out to be in need of amendment orabandonment as new insights were gained and in some cases as new distinctionswere invented or discovered. The issue is not whether moral ideas are critical,surface, conventional, socially accepted, religious, traditional or howeverinitiated; the issue is whether they are good principles or not. But discerningthat takes ongoing dialogue and judgment, not some replacement for thosethings, such as mere voting or appeal to formal or supposedly objectiverules, or even acceptance by prestigious law professors or publicationin influential law journals. Moral philosophy is difficult and it is anongoing precess as new ideas and distinctions come to light. Substitutingsomething easy for it is abandoning morality, not simplifying it. And itis important to keep that in mind, so that we do not have the mindset thatparticular laws, just because they have been promulgated and even upheldin court, or accepted by academia, are therefore deserving to be permanent,revered, authoritative (in a moral sense), deserving of obedience, or arein some sense always right.
The articles we read won't always have a straightforward structure.
At the beginning of An Essay Concerning Human UnderstandingLocke says that since his purpose is “to enquire into theOriginal, Certainty and Extant of human knowledge, together with thegrounds and degrees of Belief, Opinion and Assent” he is goingto begin with ideas—the materials out of which knowledge isconstructed. His first task is to “enquire into the Original ofthese Ideas…and the ways whereby the Understanding comes to befurnished with them” (I. 1. 3. p. 44). The role of Book I of theEssay is to make the case that being innate is not a way inwhich the understanding is furnished with principles and ideas. Locketreats innateness as an empirical hypothesis and argues that there isno good evidence to support it.
I agree with Y that the skeptic's conclusion is false.
In your notes, you might make a quick outline of the article's major argumentative "pieces." Draw arrows to diagram how you think those pieces fit together.