Vietnamese areis ”ベトナム人” ¶
American areis ”アメリカ人” ¶
The meaning of "学生" is student and "会社員"is office worker.

In this case, using 'is' is because you're talking about 'Vietnamese' and 'American' as words. 'Vietnamese' is one word - so it's singular here.

However, when you're referring to the Vietnamese people or American people, you are talking about the people - multiple people so you would say, 'Vietnamese people are...' or 'American people are.../Americans are...'

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It is difficult for me to know which one to use, "Vietnamese is" or "Vietnamese are" ... ¶
Whaten ist comes to grammar, I suppose "Vietnamese are" is right but I feel like strange because I diescribe "A person" in the prievious sentence.

Similar to how deusexmachina answered already, with nationalities, we usually say '~ people': Chinese people, Spanish people, British people...
ex) Chinese people are tech-savvy. British people have a British accent.
If it ends with '~an', we don't have to say people, but we should make it plural by adding 's': Americans, Canadians, Koreans...
ex) Canadians like maple syrup. Koreans are stylish. --> we are talking about all Canadians or all Koreans.

Of course, if you're talking about one person, it would just be: American, Canadian, Korean...
ex) She is Canadian. Being a Canadian is nice because you learn English and French in school. --> we are talking about one person

However, Vietnamese areis plural in the next sentence.

Vietnamese people are ”ベトナム人” ¶
American people are ”アメリカ人” ¶
The meaning of "学生" is student and "会社員" is office worker.

It's typical to say "〇〇 people" when referring to nationalities. For example, "Japanese people are friendly" sounds better than "Japanese are friendly." I think an exception to this is if the nationality ends in -an. In this case, you can use -ans to refer to the plural. So, both of these sound okay: "Americans are friendly" and "American people are friendly." The same is true for other -an nationalities: "Italians are friendly" and "Italian people are friendly."

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It is difficult for me to know which one to use "Vietnamese is" or "Vietnamese are" ... ¶
Whaten is comes to grammar, I suppose "Vietnamese are" is right, but I feel like it's strange because I discribed "A person" in the prievious sentence.