U.S. copyright law gives the author of a work the exclusive right to make, sell or distribute copies of the work, prepare derivative works, and display the work publicly. With a few exceptions, anyone else must get the author's permission before doing any of these things. The author can also transfer his rights to someone else. The "author" is the artist who created the work, unless the work was made "for hire." Works for hire include work created by an employee as part of his job, and work created with a written agreement that it will be considered "for hire." In these cases, the person or party who hired the artist is considered the "author" under copyright law.
Copyrights generally last for the life of the artist plus 70 additional years. If multiple artists worked together on a work, the 70-year period doesn't start until the last of the authors dies. There are three exceptions to this rule: anonymous works, works made for hire, and pseudonymous works when the Copyright Office does not have the author's identity in its records. In all three cases, copyright will last for 95 years from when the work was published, or 120 years from when it was created, whichever is shorter.
In addition to the general copyright protection already discussed, U.S. copyright law protects an artist's "moral rights" in some works. These works include one-of-a-kind works and "numbered limited editions of 200 or fewer copies." The moral rights are the right of attribution, which is the right to be identified with the art you created and to not be identified with art you did not create, and the right of integrity, which protects the work against destruction or modification that is "prejudicial to the artist's honor or reputation." Unlike general copyright protections, moral rights may not be transferred (although they may be waived in writing).
Works of art are protected by copyright whether or not they are registered with the Copyright Office, but registration has several benefits. A work must be registered before the artist can sue for copyright infringement, and the artist can only win attorney fees and statutory damages for infringements that occur after registration. To register a work, fill out a copy of form VA and send it to the Copyright Office along with the current registration fee and a "deposit" of the work. (There are links to form VA and the current registration fees under Resources.) The deposit is material which the Copyright Office uses to identify a work. For published works of art you must generally send two complete copies of the work. For unpublished works, you must generally send "identifying material," which consists of photos, drawings, etc. sufficient to identify the work. But many works have different requirements, including 3-D art, oversize material, and limited edition works. To determine whether a particular work has special requirements, consult "Deposit Requirements for Registration of Claims to Copyright in Visual Arts Material" (link in References).
Like registration, a copyright notice is not required for copyright protection, but it can be helpful. A visible copyright notice reminds people that the work is protected and prevents an infringer from raising "innocent infringement" as a defense. A proper copyright notice includes the word "Copyright" or the copyright symbol, the year the work of art was first published, and the name of the copyright owner. You probably don't want to put it on the artwork itself, but there are several other options. The notice can go on the back of a work or on any backing, mounting or framing (as long as the artwork is "durably attached"). For 3-D works such as sculptures, you can also put the notice on the base. If it would be impractical to put the notice directly on the work, it can be placed "on a tag or durable label attached to the copy so that it will remain with it as it passes through commerce."
This article focuses on copyright in the U.S., but copyright in other countries can be important to artists, too. Each country has its own copyright laws, so there is no "international copyright" that automatically protects a work throughout the world. But most countries offer at least some protection to works copyrighted in the U.S. For more information, consult the U.S. Copyright Office circular "International Copyright Relations of the United States" (link in References).