Historiography is a booming field at present and you have a very wide choice of texts, which, naturally, offer slightly different takes on a variety of problems.

In terms of "learning how to research and write like an historian," and to adapt an answer I offered here a month or so ago, while there is, in my opinion, absolutely no substitute for learning how to write history by actually "doing it," instructional books of the sort you seem to be interested in do exist. Furay and Dalevouris, for example, have collaborated on a practical volume aimed at American undergraduate students which is called The Methods and Skills of History. For my money, however, this is a very inferior work relative to the more demanding (albeit less practical, more conceptual, and less tightly focused) History: An Introduction to Theory, Method and Practice, by Claus and Marriott.

If, on the other hand, you are interested in how historians think about and conceptualise the past, then the two "classic texts" for the Anglophone audience that most student historians here in the UK ought at least to be aware of are EH Carr's What is History?, first published in 1961, and Richard J. Evans's In Defence of History, first published in 1997. Carr is, obviously, very old now, but, whether or not one agrees with him, the discussion he offers has been the basis of a very high proportion of later historiographical debates, which makes hims still worth reading just to get a feel for the lie of the land. But I recommend my students read a school-to-undergraduate level basic historiographical survey – John Warren's History and the Historians (1999) – and a more up-to-date general work as well: Sarah Maza's Thinking About History, which is better rooted in more recent debates and appeared in 2017. Broadly speaking, all of these books ought to be intelligible to the non-specialist, and one might sum all of them up by saying they are focused on considering what history "is" and how one might "do" [meaning research and write] history. The key output they advance which comes as something of a surprise to the non-specialist is that history is not "everything that happened in the past," or even the raw information that historians find in various places, such as archival sources. Rather, they claim that history is a product – the output of the human intervention that is required to analyse, evaluate and interpret that information.

If you want to pursue things beyond these beginner-level interrogations of our subject, start to understand historical traditions that go well outside those of the English-speaking world, and dive into some of the current hot topic-areas, such as environmental history, then in my view the best general work currently available is the multi-author, five-volume, Oxford History of Historical Writing (2011). But I should add that although it comprises dozens of introductory surveys of various areas, it is still very much written at and for the professional level.