How should I go about structuring an introduction to an essay (not source-based)?

First of all, it is most important to define the key terms in the question. For example, lets look at the question 'How successful were the changes made to Tudor government finances in the years 1536-53?'

The key terms in this question would be 'Tudor government finances', and what would make them 'successful'. So, start by explaining what your interpretation of 'Tudor government finances' are (e.g. 'Management and of the crown and government’s wealth'), and what defines a 'successful' financial policy (e.g. 'increased organisation, more effective procedures, financial stability').

You then ought to outline roughly how your argument will commence. For example, with this question, it may be useful to take into account those who were leading the financial changes, and so something along the lines of 'The extent of success of the changes to finance were dependent on the ambition of the person in charge' may be useful if you are going to structure your argument chronologically, dealing with different leaders such as Cromwell, the Duke of Somerset and the Duke of Northumberland.

Finally, your introduction ought to give a clue as to what your final judgement will be. Therefore, with the knowledge that Cromwell knew that his position was wholly dependent on satisfying Henry VIII's demands, it is likely that he would have carried out a policy to raise funds for Henry during his time in office. However, by contrast, the fact that the aims and ambitions of Somerset were wholly different to those of Cromwell, as he was more interested in military glory than financial success, makes the likelihood of his financial policies being 'successful' much less.