A run-up chapter that clears the ground before the real subject starts. It settles what the word 'method' means, why the topic is worth studying, what earlier books exist on it, and what people mean by 'the conditions of the imams'.
The plain Arabic sense of the word. Manhaj (منهج), and its sister forms minhaj and nahj, mean a clear or straight road. Ibn Manzur glosses minhaj as 'the clear road', and the Qur'an pairs it with shir'a in 5:48. So the word points to a path you can actually see.
The technical sense. Baqa'i defines manahij al-muhaddithin as the routes the hadith scholars take in narrating hadiths, commenting on them, and compiling them, according to set conditions. He then explains why each of those three words is in his definition.
Ten reasons the subject pays off. Among them: you can tell a connected chain from a broken one, you get better at takhrij (tracing a hadith to the books that carry it), you learn why two imams grade the same hadith differently, and you can read a compiler's book the way he meant it to be read.
A survey of what has already been written. He lists roughly two dozen works devoted to the subject, from Abu Dawud's letter to the people of Mecca and al-Tirmidhi's Kitab al-'Ilal down to modern studies, then a second batch of books that only cover part of it.
Two general research tools the hadith scholars used, which other fields use too. Istiqra' (استقراء), gathering every case to see the pattern, and muqarana (مقارنة), setting versions side by side. Baqa'i's point is that what made their use of these tools different was the honesty they brought to them.
A key term, easy to misread. 'The conditions of the imams' does NOT mean the general requirements for accepting a hadith. It means the standard a particular compiler held himself to for the narrators he put in his own book. You learn it either from his own statement or by combing through the book.
A warning that follows straight on. Guessing at an imam's standard without actually working through his book is worthless, and whoever builds on guesswork goes badly wrong. He also notes that the methods of compiling were covered in his earlier book on takhrij (tracing hadiths to their sources), so he leaves them out here.