If you want to copyright a t-shirt or a specific part of a t-shirt design, then you should be aware of how copyright works and how it can relate to different elements you may have on a shirt. Any original artwork that you wish to feature on a t-shirt is already protected by copyright law and you own the copyright on it by virtue of creating it. You cannot copyright an idea for a t-shirt, since ideas cannot be protected by copyright, nor can you copyright a method for creating or printing t-shirts. While you can copyright an image of a t-shirt, you should use a trademark or service mark to protect a logo you may want to print on the t-shirt.
International copyright law provides protection for works of art and artistic creations. This copyright protection exists at the moment a work is created, and so you can copyright a t-shirt design simply by creating the image on the shirt. If you want to produce a t-shirt featuring a piece of art that is an original creation by you, then you need only create that artwork and you own the copyright on it. You may want to register a copyright for an image to have greater protection, and this can be done through a government or private agency in your country.
You cannot copyright a t-shirt idea, however, since ideas are not protected under copyright law. Copyright law will also not protect a vague or general design for a t-shirt, such as the idea of having white text printed on a black t-shirt. You also cannot copyright the t-shirt printing process, since this would be protected by a patent. Contact a patent office in your country for more information on this process. Only original works of art and artistic creations can be protected by a copyright.
If you want to copyright a t-shirt that includes a business logo, then you should register that logo as a trademark or service mark. Copyright protection only extends to artistic works, and anything that represents your business would need to be protected under trademark law. You should include a trademark indicator such as ™ and register your trademark with the appropriate government agency for the country in which you live. If you live in the US, for example, then you can copyright a t-shirt's art and officially register that copyright with the US Copyright Office, and trademark a business logo with the US Patent and Trademark Office.