Generally, you must be able to demonstrate a basic level of reading, writing and understanding English to qualify for naturalization, which is the process of applying for US citizenship. You will also need to have a knowledge of US history and government. You can get a copy of the Sample U.S. History and Government Questions on the USCIS website.
The English language requirements do not apply to people over 50 years old who have been living in the United States for more than 20 years in lawful permanent resident status. The requirements are also waived for people over 55 years old who have been living in the United States for more than 15 years in lawful permanent resident status. There are also waivers available for people who are physically or developmentally disabled or who have a mental impairment.
"Do you need to know good English to become a US citizen?" The literal answer is "no."
A naturalization applicant only needs to demonstrate “An understanding of the English language, including an ability to read, write, and speak...simple words and phrases...in ordinary usage in the English language....”