的 [de] is such a widely used auxiliary word; it appears everywhere in Chinese news articles, as well as in daily speech. Native speakers of every language rely almost entirely on their own habits for order in their speech, and therefore never need to think of explicit rules of grammar, such as the title of this article mentions. But, for people who learn Chinese as a foreign language, learning (and consciously remembering) grammar rules is a necessity.
的 [de] indicates possession to the antecedent.
我的（my）, 他的（his）, 她的（her）, 他们的（their）, 学校的（the school’s), 公司的（the company’s）
But, if the center word is a kinsfolk, the name of an organization, a home or a country, then 的[de] is optional because the association is obvious enough to imply possession.
For example：我的爸爸 = 我爸爸（my dad）
我的姨妈 = 我姨妈（my aunt）
我的家 = 我家（my home）
我们的学校 = 我们学校（our company）
你们的国家 = 你们国家（your country）
美国的政府 = 美国政府（American government）
的 [de] can be attached to a variety of words or phrases (in linguistics terms, it’s called a notional word or phrase), and the result will function as a noun, or a noun phrase.
这是我的。(attached to a pronoun)
This is mine.
我要红色的。(attached to an adjective)
I want the red one.
这台电脑是学校的。(attached to a noun)
This computer is the school’s.
今天来参加派对的都是美国人。(attached to a verb-object phrase)
The people who attended the party today were all Americans.
我说的是真的。(attached to the verb 说)
What I said is true.
是…..的 is a sentence structure which is used to express emphasis.
Examples for affirmative patterns:
我是昨天到上海的。（Emphasizing the time）
It was yesterday when I arrived Shanghai.
我是坐地铁来公司的。（Emphasizing the way or manner）
It was by subway that I traveled to the company.
我和他是在酒吧上认识的。（Emphasizing the place）
It was in the bar that I met him.
是王先生开车送我回家的。（Emphasizing the person）
It was Mr. Wang who drove me home.
Examples for negative patterns：
我不是去年到上海的。（Emphasizing the time）
It was not last year when I arrived in Shanghai.
我不是坐地铁来公司的。（Emphasizing the way or manner）
It was not by subway that I traveled to the company.
我和他不是在酒吧上认识的。（Emphasizing the place）
It wasn’t in the bar that I met him.
不是王先生开车送我回家的。（Emphasizing the person）
It was not Mr. Wang who drove me home.
Putting 的 at the end of a statement can strengthen the affirmative tone.
I know this!
Your dream will come true!
No worries, he’s going be fine.
什么的 is a fixed structure, placed after juxtaposed words or phrases, which means the same as ‘and so on’ or ‘etcetera’ in English.
She likes cats, dogs, pigs, and so on.
We talked about movies, novels, music and so on.
On the weekend, I like watching TV, surfing the internet, shopping etc.
的 can be used to punctuate a short response to a yes/no question.
Including 的 in this manner has no significant effect on the meaning, it just subtly modifies the tone, to a nicer, milder tone.
我们去公园好吗？Shall we go to park?
你是中国人吗？ Are you Chinese?
我可以坐在这里吗？ May I sit here?