How do native speakers structure their essays? When analyzing Chinese speeches or essays, I often have difficulty understanding how their the authors organized their ideas. 

In North America, for example, a common template for writing an essay is the five-paragraph essay. This organizes the paragraphs and the sentences within each paragraph. Most English-language writing in academia follows a somewhat similar structure to this.

Do Chinese follow any particular structures when planning speeches or essays?
Are there any ancient scholars who heavily influenced this structure?
The Chinese have a device called 起承转合. First you start(起) narrating on some topic. Then you continue(承) to develop the topic with added material. Then you turn(转) the narrative, either by seeking different aspects, or creating conflicts and resolving them. Finally you conclude(合) the topic.

Often it goes like this:

(起) New study shows that spanking is bad for children...
(承) The study is conducted by Harvard and it goes like... 
(转) Some may say "I was spanked as a child, and I turn out to be fine." They are wrong because...
(合) So it's better not to spank our children...


It also work in poems and songs. Here is a modern example, a song by by 张玮玮, titled 《织毛衣》 

(起)我深深地爱着你
(承)你却爱着一个傻逼
(转)傻逼却不爱你
(合)你比傻逼还傻逼


This idea has its classic roots, so we can see it being used in classical poems as well. For example, 《登高》 by 杜甫, my all time favorite:

(起)风急天高猿啸哀，渚清沙白鸟飞回。
(承)无边落木萧萧下，不尽长江滚滚来。
(转)万里悲秋常作客，百年多病独登台。
(合)艰难苦恨繁霜鬓，潦倒新停浊酒杯。


It's rather akin to the Hollywood three-act structure, where you plan the plot, develop the plot, reach the climax, then draw the happy ending. 

Note that it's just one of the common devices that could be used on any type of writing. As for scientific theses, I think most of them try to follow western standards.