I perform legal translations, represent authors and translators in various countries. Every once in a while they come across a brilliant article or a book and ask, "Would it be legal to translate it and post the translation online?" No, not in the U.S. Not unless the original work is in a public domain or you have the original author's (or other copyright holder's) permission. Without such permission, you could only publish excerpts from that translation for non-commercial use under the "fair use" exemption in the US copyright law.
Copyright law of other countries generally follows the same pattern, even though there is really no such thing as international copyright law. A claim of copyright infringement is governed by the laws of the country where the alleged infringement occurred. Nevertheless, most countries have signed international IP treaties and conventions that offer copyright protection to foreign works. Berne Convention largely standardized copyright law among the 172 countries that signed it. This Convention introduced the concept that a copyright exists the moment a work is created, even if the copyright is not formally registered.
Under the U.S. copyright law, a translation is a "derivative work" that is based on the original work. Other examples of derivative works are: motion picture versions of literary material or plays, art reproductions, “new editions” of preexisting works, a motion picture based on a play or novel, a drawing based on a photograph, a new version of an existing computer program, etc. The exclusive right to prepare derivative works belongs to the original copyright owner (U.S. Code 17 § 106 (2)). That's normally the author, unless the author sold copyright to somebody else. E.g., if the author wrote the piece as work for hire, then the employer will own copyright. Author could have sold copyright to publisher. Or, author could have licensed exclusive publication rights that last some years. Bottom line being, you need to determine who holds the rights to the original work and ask permission prior to publishing your translation.
Without the author's (or other rights holder's) permission, you can still use parts of the original work to publish derivative works if it falls within the "fair use" exemption to the exclusive rights of the copyright holder. (U.S.C. 17 § 107). It gives you the right to use portions of others' work for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research. Such limited use will not be considered copyright infringement even if you do not have the author's permission, especially if the use is noncommercial. Basically, the less of the copyrighted work you use and the more benign the purpose of your use, the higher likelihood that it will fall within the "fair use."
In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include —
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(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 upon the potential market for or value of the copyrighted work.
Another exception that would allow you to post translation is if the original work is in the public domain. For example, a translation of an ancient epic poem. See Copyright Term and the Public Domain in the United States.
