If what you want to quote is in a magazine, write directly to the magazine for permission. If the publisher bought only first or one-time rights, the author owns the copyright and he/she is the only one who can grant permission. In that case, the magazine will usually forward your request to the copyright holder if they don’t own it. You can ask them to do that in your request letter.
If you find the quote you want to use in a book, check the copyright date in the book. If older than 75 years, you can use it without permission. If less than 70 years, determine whether the copyright is in the name of the publisher or author (copyright notice is usually on the back of the title page (sometimes on the front of that page). If copyrighted in the publisher’s name, send the letter asking permission to them. If in the author’s name, prepare the permission letter addressed to the author in a separate envelope and include it in a letter to the publisher asking them to forward it to the author.
If the book publisher has gone out of business, do not assume you can go ahead and use the material without permission. Someone still owns or controls those copyrights and you need to get permission before using them. You may then contact the Copyright Information Office. They will be able to tell you who the current copyright owner is for that particular book.
Prose Quotations: The policies of publishers vary regarding quoting from their publications without specific permission. Usually you need not write for permission to quote phrases or brief sentences. Publishers do not want to be bothered by requests to quote just a few words. The nature and importance of the material to be quoted will give guidance at this point. The two factors every publisher expects are (1) accuracy in quoting, and (2) the giving of proper credit.