In cases where use of a copyrighted work exceeds what would reasonably considered to be a fair use and no other copyright exception applies to your use, or if a publisher insists on your obtaining written permissions as a condition for publication, or if any contract or license associated with the copyrighted work requires that permission be obtained, you will need to obtain permissions from rightsholders.
One way is to contact directly the current copyright holder if you can identify and locate that entity, which may be an individual or individuals or an organization. Often it is a publisher. This may or may not involve payment. In some cases permissions may be obtained through the Copyright Clearance Center or another collective management organization that offers permissions services for works it manages. For international works, IFRRO is the main international network of collective management organizations that facilitates permissions for copyrighted material.
It is sometimes difficult obtain permission for older works, works of small publishers, works of publishers that no longer exist, and for many types of foreign works. It may be difficult even to identify or locate a current copyright holder for older works. In cases where it is not possible to obtain permission, or even to identify or locate a current copyright holder, authors need to be prepared to make realistic decisions about use of a particular work. In traditional publishing scenarios, often your publisher is the “gatekeeper” on this issue. If the publisher is willing to proceed without permissions, that is the publisher’s decision. If the publisher insists on your obtaining permissions, then it becomes your responsibility to obtain them or to forego inclusion of the work.
Remember that using short excerpts of published works as quotations, with attribution, is generally accepted as a fair use and does not require permission. There are more considerations for unpublished works, such as the right of consent to first publication, privacy, and confidentiality issues.
Copyright permission requests and permissions should be made in writing. Email is an acceptable form of communication. This is a basic template for a permissions request for an article or book publication.