Yet again, this is a book aimed at professional historians, rather than at the general public. So an important aspect of your task as a reader is to think about the questions that Elliott poses and the answers that he comes up with. Remember that good history isn't just retelling the details of what happened in the past; it's making sense of the past, understanding how and why things played out as they did, and defining what changed as a result.
Here the starting point is to develop for yourself thumb-nail sketches of the two main characters. Who were Richelieu and Olivares? What were their social and cultural backgrounds? What training did they have for power politics? What was the basis of their power, and how did they hang on to it? After all, neither was a king or elected official; how did they come to play such big roles?
Then think about the outcomes. After a long struggle, Richelieu won and Olivares lost, raising a series of further questions: What exactly was this long struggle? What was being fought over, and what were the methods of the struggle? What events marked the ultimate triumph/defeat?
This leads to one of Elliott's basic claims (spoiler alert...), that Richelieu won by a very narrow margin, and that France rather than Spain might well have failed first. Think about this argument: what steps does it involve, and how does Elliott back it up? One argument that he makes centers on the similar problems and challenges that all seventeenth-century governments faced. What were these?
We've discussed at length the costs of early modern warfare, as a by-product of the military revolution. How important were these costs for France and Spain? What kinds of choices did they require? How difficult was it for these states to sustain their military efforts? What had to be sacrificed in doing so?
Finally, think about these two men as personalities. What was their emotional make-up? What kinds of religious commitments did they display, and what were the limits on their piety? What were their personal lives like? How similar to us do they seem?
