The papers were published simultaneously in the form of a debate with each side stating an issue and defending it from the other side. The papeback Mentor edition edited by Ralph Ketchum has a chronology of publication in the appendix. If you read both sets of papers interleaved in strict order of publication, you can watch the ebb and flow, the point and counterpoint, of the debate over ratification of the Constitution in New York. For example, Hamilton will make a point in a "Federalist Paper" that is answered by "Brutus" in an "Anti-Federalist Paper", which in turn receives a riposte from Madison in yet another "Federalist Paper". Reading them this way clarifies the scope of the debate.
Eighteenth Century English is quite a trial for today's readers who are used to a shorter sentence structure. I've found that one has to read a given paragraph 3 to 5 times to distill all the meaning the writer has poured into it. But it's worth the effort. Just don't rush it.
Hear Here!
In fact this should be a requirement for graduation from High School!