In my experience, not 1 single 对外汉语教师 can explain these two words, the most popular-used, to the students, unfortunately, including myself. Can anyone explains is this sequence: 1. basic/fundamental meaning/function/usage, 2. extended meaning/function/usage (might be a few), and 3. special meaning/function/usage (very different from or even contrary to the basic one)? So as not to mislead the students furthermore which is exactly what I am facing now.
的 can be used to describe thing as follow [description]的[thing]. [description] is component used to describe thing. [thing] is component used to denote described thing. For example, 美麗的風景([description]的[thing], where [description] is 美麗, [thing] is 風景). Here [description] (美麗) is used to describe thing. [thing] (風景) is component used to denote described thing. 美麗的風景 means beautiful scenery.
的 can be used to denote affirmation or intensified tone as follow [component]的. [component] is component that people used to express what they think. For example, 事情不是這樣的([component] is 事情不是這樣). [component] (事情不是這樣) is used to express what people want to express. 的 is used to denote intensified tone. 事情不是這樣的 is used to tell people that thing is not what people think.
了 can be used to show that thing have happened as follow [description]了. [description] is used to describe something happened. For example, 我喝完了([description] is 我喝完). [description] (我喝完) is used to describe thing have happened. 我喝完了 means I have finished to drink something.
了 is a "change of state" particle. Some people confuse it with being a "past tense" particle, but it isn't that. It is however mostly used in sentences to convey the idea of something having happened in the past.
For example： 你吃午餐了吗？ English Translation: Have you eaten lunch? Literal Translation: You(你） eat(吃) lunch(午餐) (change state particle)(了) (yes or no question particle)(吗)?
Change of state doesn't always only convey that the phrase/action before the 了 happened at some moment in the past. It can be used to refer to the future aswell. However, in my experience, it's usually used to express a state in the past that is no longer the case, and would only be used to refer to the future if it is explicitly mentioned you are referring to the future in the sentence or in context, or if it's such a common phrase that people already assume you refer to a state in the future with that sentence.
Outside of it's typical use, 了 can also be used to form words like：
了解 (liǎojiě), meaning: to understand
的 can be used for various purposes, the most common of which is to show ownership.
For example：我爱我的妈妈 English / Literal Translation: I love my mom
Another example is it's usage is in the
是...的structure to express either a statement or ask a question in the past that also focuses on a peace of information RIGHT after the 是.
Example 1: 你是什么时候回家的? English Translation: When did you return home? Literal Translation: You is when return home (procession particle 的) Example 2: 我是八点回家的 English Translation: I returned home at 8 Literal Translation: I is 8 return home (procession particle 的)
I explained the
是...的structure above. It's not limited to this structure, though I wouldn't want to overload a newcommer.
special meaning/function/usage (very different from or even contrary to the basic one)：
Example: 你的中文比我的好 English Translation: Your Chinese is better than mine Literal Translation: Your Chinese compared to Mine (assumed/silent "More") good
There are 2 的's in this sentence. The first one refers to "your Chinese"/
你的中文. The second one doesn't have the word "Chinese" after it （
我的）. This is an example of where you don't need to include what the character 的 is showing procession of because it's inferred from the context.