This is a great question and one that is very important to ask. Let me make a few points that will help you get started.
First, we have to come to terms with the fact that often times the majority, who have power, do not accurately preserve the stories of the minority. This is the case in the segregation of baseball. With this said, all is not lost.
Second, there are books on this topic and I would say that if you look through the bibliographies, you will get some good primary and secondary sources. Here are a few title that you may want to examine.
- Don Rogosin. Invisible Men: Life in Baseball's Negro League.
- Jules Tygiel. Baseball's Greatest Experiment: Jackie Robinson and his Legacy.
- John Klima. Willie's Boys: The 1948 Birmingham Black Barons, The Last Negro League World Series.
These three books should get you started. The first one comes with a CD. The second will have tons of primary sources, because it will contain the words of Jackie Robinson, who was the first African American baseball player in a non-Negro league. In addition, you can read about the historical context of the time period to get more insights about what the society was like. Another way to get primary sources is to look through newspaper archive. By doing key word searches, you will gain some great insights.