Before post-colonialism became the new sheriff in town, most 'theoretically interested' historians, if you excuse this phrase, were Marxists or classic social historians prioritising economics over all else. So a rather laconic answer to your question 'what the practice of history used to look like' before post-colonialism is: it looked like sociology. Now it looks like anthropology. But, often, it does not. Because most historians are not theoretically interested, as I will try to make clear at the end.

In intellectual history, if you want to understand what a given author means, it is often very much related to understanding what pissed him/her off in the first place to write this text. If you look at key works of post-colonial historians (Gyan Prakash is a good example), you see that they are generally arguing against social history and Marxism. This is because before the advent of the post-colonial studies, most 'theoretically interested' historians focused on economic interests and class structures. This, they believed, was particularly relevant to the practice of history of former colonies because the fate of it was shaped by colonialism, which was nothing but an advanced form of imperialism, which in turn was 'the last stage of capitalism' as Lenin put it. If you look at works of social and economic history before the post-colonial turn, you will see an interest in numbers, a drive for quantification (not the kind you get in other social sciences though, since our data is typically quite different for that kind of research) all for understanding the socioeconomic structure of a given society, or even of the world at large. Famously (or notoriously), those like Immanuel Wallerstein (not a Marxist per se) and historians influenced by him saw the globe as their unit of analysis and sought to understand its history from the 16th century to our present-day as a function of certain economic relationships.

The domination of sociologically-informed methods took forms such as these: Italy had fascism because it had a certain type of middle class and an economic crisis, the US had slavery because of certain economic facts (which caused a gigantic and increasingly political debate over the actual profitability of slavery), Turkey (insert any other non-Westernised country here) did not have democracy because it did not have middle classes, John Locke was a liberal (spoiler: he was not) because he was a slave-owning bourgeois... Post-colonialists found these too simplistic. This is part of the reason they are so allergic to what they call meta-narratives. So, after the post-colonial turn, historians speak of classes and economic interests more rarely. This change is evident in one case, the Subaltern Studies, which has increasingly moved from an E. P. Thompson type of culturalist-leaning Marxism to a post-colonial analysis of discourse. This is why scholars with Marxist sympathies like Sumit Sarkar and Arif Dirlik (who I genuinely think was more Marxist than Marx himself; he has a book called the Postcolonial Aura to criticise the turn away from Marxism) charge the post-colonial turn with focusing on more 'trivial matters' like identity instead of devoting time and effort to studying 'objective' class relations. Objective is an apposite word in this context. Before the post-colonial turn, most 'theoretically interested' historians were interested in objective data such as tariffs and rising/falling urbanisation percentages, whereas now they consider 'subjective' things such as identities and ideologies, without trying to reduce the latter to the former.

The kinds of social and economic history that I have been delineating, in turn, clashed with histories inspired by 'modernisation theory' and with what I shall call Rankean political history. This theory was more cultural than what came later, in that it gave the West a leading role in world history at least in part due to cultural developments within it. But it too used sociological concepts like classes, urbanisation, etc. If you were wondering what came even before that... Perhaps this would go as far back in history as Leopold von Ranke, Edward Gibbon, David Hume, or... Thucydides? I find it ironical that after all the theoretical debates, what an actual historian does today is not altogether different from what Thucydides set about doing in Ancient Greece. I think you would enjoy reading any of these chaps. This is because they do not really depend on any such theoretical construct. They certainly had presuppositions, such as there being a progressive trend in history or the West representing the peak of that (excluding Thucydides of course), but they did not have clear-cut concepts like classes, nor did they build their accounts on difference, identities, the oppressed ones, etc. They focus on whatever they were studying (which was typically high politics of a given period) and in light of archival data, they try to come up with a rational, plausible story about what happened and what were the intentions of the actors involved. The sociologist Daniel Little has a short review of Hume's the History of England from a methodological perspective if you are interested. Bear in mind that Little is a sociologist (an excellent one too, but ignore the bit about Hume and causation at the end since Hume did not deny the usefulness of causation in his philosophy, contrary to what Little seems to think) so he wants to see sociological reasoning in Hume and seems disappointed when all he finds is good old empirical history going case-by-case and asking about the intentions and motivations of individuals. So this is actually a good case of showing differences between the typical ways historians operate(d) and the way sociologists and sociologically-informed historians (social historians before the post-colonial turn, basically) judged their work.

(1/2, to be continued below)