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.