Generally, the author of a work owns the copyright. Copyright is granted automatically when a work is created; authors do not need to register to be protected by copyright. However, registration is required in order to bring a lawsuit for copyright infringement.
There are some exceptions to this, such as the work for hire doctrine, which relates to works made during the course of an employment contract. Works made for hire include works made by an employee as part of their job, or works commissioned as part of a collective work, provided that the author has signed a contract to this effect.
For works made as part of a collective work such as an anthology, absent an agreement otherwise, authors are presumed to own their contribution. Each author is able to exercise their exclusive rights over their work.
For works made by two or more authors as part of a joint work, such as an article with multiple co-authors, authors are presumed to be co-owners of the copyright. Joint authors retain non-exclusive rights over the work. Joint ownership can be complex, and authors may want to discuss copyright ownership at the outset of a project.
One way to determine ownership of a work is to look for a copyright notice. Copyright notices are not required to establish copyright, but they are present on many published works. You can also check the Copyright Catalog, or ask the United States Copyright Office to conduct a search for you [pdf].