What should I do to write an A/A* grade essay?

In terms of structure I think it's important to break down the question into manageable chunks. This can be explained in the introduction - from my experience it's usually best practice to write an introduction for essay questions, although they're often superfluous for source comparison questions. For example, if we take the example essay question "Did Bismarck succeed in subduing German socialism during his reign as chancellor, 1871-1890?" I would break the question down in two different ways. Firstly, because Bismarck made a notable political turnabout in 1878 which affected his policy toward socialism I would break the question down via time period, that is into a period from 1871-1878 and another from 1878-1890. Secondly, I would break each of these time periods down by the more obvious division suggested by the question, that is whether or not Bismarck was successful. This provides four paragraphs where evidence specific to each segment can be deployed, making constructing the bulk of the essay much easier. For higher level answers it's important to balance the weight of evidence between paragraphs. In the conclusion a judgement can usually be reached by summarising the result of each of the previous paragraphs, and writing no more than two or three sentences on the relative merit of each argument.
In regard to what evidence is effective, it's often useful to employ statistics to support your argument. While memorising this information might sound daunting at first I've often found that particularly convincing evidence can usually be cross-deployed across multiple essays (i.e. evidence used in open-book practice essays will likely come in handy during exams). I'd advise that you set aside a page in your notebook to jot down convincing statistical evidence as you come across it, to avoid having to collate it during study leave.