As noted in the Copy(right)s: The Basics section, registering for copyright is not necessary in order to have copyright protection over your works - copyright is immediate for original works in a fixed, tangible form. There are, however, some benefits to formally registering your copyright, and these should be taken into consideration when deciding whether or not to register your work with the U.S. Copyright Office.
Formally registering your copyright with the U.S. Copyright Office is a both a defensive and offensive measure. It is defensive because it puts the world on notice that you are claiming rights in and to your work. It also makes it easier for someone seeking to use your work to find you in order to ask permission.
Registering your copyright is also offensive. Registering your work is now a prerequisite to filing a copyright infringement lawsuit, and you may get some additional benefits under the law (the ability to seek statutory damages and attorneys' fees) if you register promptly. It is also helpful to register your work if you need to file DMCA take-down notices, or otherwise enforce your rights on the web because it serves as an objective measure that you are claiming ownership rights in your original, creative work. Below are the general benefits to formally registering your copyright:
For more information on the benefits of registering for copyright, see the "Copyright Registration" section (p.5) of Circular 1, Copyright Basics.
If formal registration of copyright seems best for your work, go to the U.S. Copyright Office's Registration Portal and choose the type of work you want to register for copyright. You can either register for copyright online (processing time 6-10 months) or using a paper form (processing time 10-15 months).
The U.S. Copyright Office is actively modernizing its procedures, and is shifting away from paper registrations. To avoid processing delays, it is highly recommended that you utilize the Copyright Office's Online Registration Portal for registration and deposit.
You will be required to submit two copies of your work in order to be registered. The copy must be the "best edition" of the work you wish to copyright and will not be returned. See Circular 7d for more information on mandatory deposit.
For some unpublished works being prepared for commercial distribution, you can preregister for copyright. Preregistration does not substitute for registration, and does not carry many of the same benefits of full registration. Preregistration simply acts as a placeholder indicating a future intent to register. If you have preregistered your work and become aware of a copyright violation, you must register for copyright within one month of becoming aware of the infringement. See Preregistration FAQ for more information.
For any other questions, see copyright.gov's FAQ for registering a work.
For more information on registering a work, see the US Copyright Office's "Registering a Work" page.