after 3 years later, I have to say, why I ask this question, is I still cannot grasp how to use the right 'article word'. sometimes, a noun will use an article, sometimes, a noun could not(or omit) the article word before it. there aren't a formula for this.
There is actually a "formula" for how to use articles in English. There are a set of rules that have evolved for when a definite or indefinite article is appropriate. Yes, there are special cases; but it's not as difficult as say, memorizing the gender of nouns in some Romance languages.
You can determine which article to place in front of almost any noun by answering three questions:
A noun is countable if you can have more than one instance of it. I can have three apples, so apple is a countable noun. Luggage is an uncountable noun. Many words can have different countable and uncountable meanings.
2. Is it singular or plural?
Just ask the question: am I referring to more than one instance of something?
3. Is it definite or indefinite?
A noun is definite if it is clear what specific thing you are referring to. Otherwise it is indefinite.
After you answer those questions you can determine which article to use with this table:
countable singular the a, an
countable plural the (don't use an article)
uncountable the (don't use an article)
Notice the rule of thumb: if the noun is definite, use the article the; if it is indefinite it never takes the article the.
Here's some examples given on that University of Toronto page I referenced:
countable singular definite
I need to study hardest for the exam that I write next Wednesday.
countable singular indefinite
I have an exam to write this afternoon, and then my summer holiday finally begins.
countable plural definite
The exams that I wrote last year were much easier.
countable plural indefinite
Exams are an inescapable fact of life for most university students.
uncountable singular definite
The importance of studying hard cannot be exaggerated.
uncountable singular indefinite
Do not attach importance to memorizing facts.
There are several special cases in the use of the definite article. I won't go into detail here, but they have to do with special classes of nouns and modified nouns. The rules are actually pretty regular with only a few edge-cases.