Writing a paper is the hard part; copyrighting one is surprisingly easy. You have a de facto copyright from the time the paper is completed, but registering your copyright with the U.S. Copyright Office makes it easier to defend legally. You can even hire someone else to create the paper for you and then copyright the result, under certain conditions.
A copyright-able paper begins with an original thought or observation, so think about the idea or ideas you want to express in the paper. You cannot copyright ideas or material already copyrighted by someone else, so you must say something original in your paper or express an old idea in a new way. If you want to be certain your idea is original, you can search the U.S. Copyright Office's database of existing copyrights for anything similar.
Create the Paper
Next, write your paper or hire someone to write it. You can copyright a paper someone else wrote if the writer is your employee, or if you specifically hired that person to write it. These are called "works for hire." If the writer is not your employee, you must have him or her sign a contract saying the paper is a work for hire and you can copyright it. Consider having a lawyer draft the contract, to reduce the risk of a legal challenge to your ownership.
De Facto Copyright
Once you've written the paper, you are automatically considered to have a copyright, even if you do nothing else. This is also the case if the writer is your employee or the paper is a work for hire. You might find it difficult to defend your copyright in court, though, especially if you haven't taken any steps to date your document. Mailing a copy to yourself in a sealed envelope, or having the finished document notarized, are two easy and inexpensive ways to protect yourself against a later, rival claim on a similar idea.
If you publish the paper, you will have to record your work by sending two copies of it to the U.S. Copyright Office within three months of publication. If you did not write the paper yourself, you should also submit your work for hire contract. Finally, you should register your paper with the U.S. Copyright Office. This isn't mandatory, but you can't sue someone for infringement until you register. Also, registration serves as prima facie evidence that you own the copyright and U.S. Customs will be able to protect your material from illegal importation. To register, you'll fill out an application, pay a fee and file a copy of your paper with the Copyright Office.