How do historians use primary sources to make arguements about the past?
Historians use primary sources to construct arguments about things that happened. They interpret speeches, letters, court records, private journals, and a host of other written material to try to reconstruct events, determine the motives of historical actors, and even to ascertain what underlying forces affected historical events. Historians analyze these sources for biases, hopefully not accepting what they have to say at face value. But they use them as evidence to construct a case in a way that some historians have likened to a courtroom attorney, using them to try to determine what happened, why it happened, and even how people viewed things that happened in the past.
The documents and evidence that a historian chooses can have a serious effect on the types of arguments they make. For instance, historians who studied the American Revolution by reading the writings of such leaders as Thomas Jefferson or George Washington might look at the event quite differently than one who studied discipline records of militia units or local revolutionary committees. It should be noted, in conclusion, that when they work, historians also engage with the relevant historiography, meaning they read what other historians have written on the topic they are studying. They build off of (or argue against) these earlier works by either pointing to new evidence or reading old primary source evidence in new ways.