The answer is that it depends on the situation. It is always legal to quote an oral statement uttered by the speaker in public. Anything published in the United States prior to January 1, 1923 is in the public domain and no permission is needed. Additionally, anything published in the United States before January 1, 1964 for which the copyright has not been renewed is in the public domain.
For written works still protected by copyright an author may quote or paraphrase brief passages provided they are making “fair use” of the quoted material. What is fair use is based on a balancing test involving four separate factors. The factors to be considered are:
1)The purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes and whether such use is “transformative” as opposed to merely “derivative”;
2) The nature of the copyrighted work;
3) The amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
4) The effect of the use on the existing or potential market value of the copyrighted work.
If one is using the quote for purposes other than scholarship or criticism permission may be necessary no matter how short the quoted portion of the work is.