What are at least two major approaches to the study of world history?
Being quite a vast topic, world history affords a historian a number of different approaches with which to study it. Perhaps the most common approach to history is the definition of particular areas of history. This can either be understood as a study of different aspects of society (intellectual history, political history, social history, economic history) or in how the different parts of world interact with each other (forreign relations/clashes between cultures). An intellectual history is concerned with the question of how ideas influence culture and have done so throughout history. In this case, the nature of the ideas can run the range from the political, social, and economic, to the philosophical, theological, and scientific. In the second case, historians can specialize in specific times of history (i.e. French Revolution, Crusades), all of which represent interactions of different kinds. Those interactions can say a great deal about the nature of the societies involved.
Another approach to world history springs not as much from the content itself, but rather the approach to that content. For example, the Annales School was a school of historiography that flourished primarily in France between the wars. Its emphasis was on social history, but specifically on the writing of "total history." In "total history," all areas of history are incorporated, and all levels of society are considered in the formation of the historical narrative. At the same time, another approach to history is known as the "Whig Interpretation of History," which entails the idea that history is the story of great men. Examples of this approach are numerous, and the prevalence of biographies in the history sections of bookstores is testimony to its influence. Of course, there are numerous examples that fall in between these two extremes.
There are many approaches to history, but since you ask only for two, I will comply.
1. There is intellectual history. This is the history of ideas, such as philosophy, theology, and any other thought. So, a historian from this school of thought would study the great thinkers of a society and draw conclusions.
2. There is also social history. These scholars are not so much concerned with what the great thinkers of a historical thought, but what people ate, where they lived, what they wore, how they spent their money, how many children they had. They deal in the mundane and come to insightful conclusions.