Although I’m a Nineteenth Century specialist, I also use Twentieth Century newspapers for teaching and research purposes. I’ve been asked about how to go about researching Post-WW2 civil rights history using historical newspapers. I can only discuss what I’ve used, which is the ProQuest historical newspapers database. There may be other good searches for articles in this time frame, and I invite suggestions. If you belong to an institution which subscribes to the ProQuest database, you’ll find that access still varies according to the newspaper subsets to which your school subscribes. For instance, my library subscribes only to the top level collection, which includes the Washington Post, Times of India, and the Atlanta Constitution, among others. I wish my school also subscribed to the Black Newspapers collection, which includes the Chicago Defender and Atlanta Daily World. All these papers would be very useful for a primary document investigation into US Civil Rights history. All the newspaper collections go back as far as possible (the Post and the Constitution start in the latter 19th century, while several of the black papers start in the 1930s) and all take readers into the 1980s or 1990s, depending on the source.
If you do not have access to ProQuest, or do not have access to the portions of Proquest that you need, then contact nearby colleges to see if they subscribe. If they do, go visit them. Generally most libraries that allow you physical access will also allow you guest access to their digital collections as long as you are physically located in their library. This advise is good for all databases, not just ProQuest. For example, I do not have access to Readex databases at my school, but nearby research institutions subscribe, so I visit them when I need access.
Since I specifically use the Atlanta Constitution and Washington Post pretty regularly, I can discuss how to use them. 20th century newspapers generally scan better than older newspapers, and thus OCR better. This means searches turn up more results. First I usually limit my search to a single newspaper at a time. Then I usually limit my searches to either a year, a few years, or a decade at a time, to limit the number of hits I get at a time. Then, like other search engines, I alter the search terms to maximize the hits I get on the topic in which I am interested. For example, in researching Emmett Till, I’d first try his full name in year of his death. Then I might try just his last name by itself which would bring up hits on his mother as well. Similarly I might use “lynch*” as a search term. The asterisk is a wild card that will return hits on lynching as well as the word lynch. Repeat the process for subsequent years, or even for preceding years to see if something turns up. The searches can be tagged and emailed for later downloading, which is a very useful feature. Be careful about emailing searches to others. I sent a large search on “electri*” to a student working on electrification, and he tossed it because he did not recognize the sender.