It would be quite difficult to learn about history if we didn't have written languages to study. Even in ancient Rome, the political figures understood that written history would preserve events for posterity. They employed paid historians in order to shape their own versions of events for future generations.
One example of how studying a written language gives insights into history is the English language. A Germanic language in origin, English absorbed significant French influence for decades following the Norman Conquest in 1066.
It is hard to believe that as many differences as there are between languages that they could all be traced back to one language of origin. I had never really thought about this until now.
Good answers above. Studying the roots, prefixes, and suffixes of a language are probably the best way to observe history--looking at when and where words were introduced in a certain time and place will reveal something about the history of that place. For example, when the French aristocrats invaded England in 1066, as mentioned above, the name of an animal in the pen or fields (cow, pig) was determined by the English peasants who tended them. Once the meat from these animals reached the French tables, the names, of course, were French (beef, pork). I, too, find this a fascinating subject.
In addition to the sterling answer provided by herappleness above, you also might like to think about how languages change as a result of cultures criss-crossing. For example, the English language as we come to know it is a result of a myriad of different cultures impinging on the original English language. Thus what we speak today is a result of so many things, for example the invasion of England in 1066 by William the Conqueror and the Imperial history of the British Empire, where terms from India and other places have become accepted into the English language. It really is a fascinating topic.
In simple terms, all languages developed from a protolanguage which is presumed to have come from a common source and place. We can take a great advantage of that fact by focusing on how this protolanguage began to branch out, and what were the causative factors that prompted it to occur. We can always go back and follow the linguistic 'hotspots' and connect the changes to other agents of change such as climate, demographic influx, and other significant developments. In turn, these latter-mentioned developments may also indicate a sudden growth spurt in intellectual development which can also associate itself to a major historical happening.
We can learn about history from languages as we study how languages were spoken in previous times and eras and gain insight as to why they spoke words in particular ways. Also, we can learn a great deal by looking at different writing systems to see the similarities and differences in our own writing to learn the ideas of others.