Make chronological notes on the period to create a timeline you can use as a reference for your essay. Plot out the important battles and events in the period, focusing your dates on your specific area of study. For example, a crucial area of study for someone focusing on the history of international relations is the 1648 Treaty of Westphalia. You can add to your timeline as you proceed, although having one will provide at-a-glance references and context for your work.
Study the rise of civilizations in the context of the period that immediately preceded them. For example, the rise Spain and the conquest of the New World were directly related to the decline of the Moorish civilization in Iberia. Similarly, the rise of England, and later Britain, in the period was caused by the end of domestic religious divisions. Civilizations do not arise from nowhere and studying their roots will provide you with a depth of understanding.
Look at the thematic links between civilizations. For example, states that were willing to tolerate religious dissent soon gained an advantage over strictly theocratic states. Louis XIV's willingness to support Protestants in the Thirty Years' War was a victory of secular realpolitik and began an age of increased secularism in foreign policy. The civilizations that prospered from 1700-1800 were those which realized this. Britain, the Netherlands and France all did. Spain did not.
Consider low politics and social developments. Essays on world civilizations tend to focus on clashes between civilizations and on the role that charismatic or powerful leaders played. To write a more successful essay, consider non-political factors, such as the rise of science, growing literacy rates and the rise of the printing press as well as technological developments. All of these underpinned civilizations and their development.
Avoid an orientalist perspective, which can be tempting in the period 1600-1800. Orientalism is a perspective which views all other cultures through the prism of western culture. Although 1600-1800 is a major period for European civilizations, do not judge Inca, Japanese or Muslim civilizations as being backward. Instead, study them with the seriousness they deserve.