Think about the article's title. If you're reading an article with the title "The State of Independent African-American Record Labels," then you should look for points that give in-depth analyses of the title.
Read other articles from the author. This gives you an idea of what he specializes in and how he treats certain subjects. Suppose you're reading about the assimilation of Haitian immigrants into American culture. The author may be a specialist in these issues, so you can read his previous articles.
Look for clues in the abstract. The abstract is a synopsis that appears just before the main sections of the article. The author gives readers an idea of what she plans to discuss.
Look for words that are often associated with the subject of the article. If you're reading an article about the history of religion in U.S. government, search for words such as "First Amendment," "separation of church and state," "freedom of religion" and "Establishment Clause."