In general, the verb "to be" is 是 whereas the verb "to do" is 做. Specifically, your examples can be translated as 我是美國人 and 你是做什麽工作的, respectively.

I am an American. 我是美国人。 What do you do？ 你是做什么(工作)的？

I am an American = 我 是 美国人。 = wǒ shì měi-guó-rén. What do you do? (What's your job) = 你 做 什么 工作? = nǐ zuò shén-me gōng-zuò?

Totally agree with above answers. Just one more supplement. What do you do? 你做什么工作？ will be more concise to your question.