My personal research approach (the little big history variant: I'm writing my Ph.D. thesis on the little big history of Tiananmen) is actually quite straightforward.
I pose a question, any question for which there is evidence available that can help me answer it really, and then follow these simple steps:
1. I try to connect my question to all the main stages in big history, which generates quite a lot of unrelated and sometimes downright absurd ideas.
2. I scrutinise these ideas, look for those with potential and for patterns running through them and throw out what I cannot use. Based on my selection, I formulated one or more hypotheses that could help me answer my question.
3. I collect data, usually from scientific papers because they are more specific, but sometimes also from academic books, that help me support, adjust or refute my hypotheses.
4. If I have to refute my hypotheses or get stuck, I go back to phase 1, the brainstorming phase, to see if I can come up with some new ideas.
I think that this approach often yields new insights, because it forces you to look at questions in a way not many people have looked before.
I don't think this approach yields the ultimate answer to the question I asked. In fact, I think that you could probably write a number of very different little big histories, all equally valid, on the same subject, because different people may emphasise different patterns and trends. I'm not a postmodernist though: I think that different little big histories are usually connected and supplement each other. This may be the case because all little big histories hark back to some of the most fundamental processes we know about and through their connections to these processes, they are connected to each other.
I hope this makes any sense.
Kind regards, Esther