Opting out of open source licenses doesn’t mean you’re opting out of copyright law.
You’ll have to check with your own legal counsel regarding your particular project, but generally speaking, the absence of a license means that default copyright laws apply. This means that you retain all rights to your source code and that nobody else may reproduce, distribute, or create derivative works from your work.
You don’t have to do anything to not offer a license, though including a copyright notice is recommended.
Copyright [year] [fullname]
Disallowing use of your code might not be what you intend by “no license.” An open-source license allows reuse of your code while retaining copyright. If your goal is to completely opt-out of copyright restrictions, try a public domain dedication.
Even in the absence of a license file, you may grant some rights in cases where you publish your source code to a site that requires accepting terms of service. For example, if you publish your source code in a public repository on GitHub, you have accepted the Terms of Service, by which you allow others to view and fork your repository; but this alone does not allow for the kinds of collaboration that people usually seek on a public code host, such as experimentation, modification, and sharing as fostered by an open source license.
If you find software that doesn’t have a license, that generally means you have no permission from the creators of the software to use, modify, or share the software. Although a code host such as GitHub may allow you to download or fork the code, this does not imply that you are permitted to use, modify, or share the software for any purpose.
Ask the maintainers nicely to add a license. Unless the software includes strong indications to the contrary, lack of a license is probably an oversight. If the software is hosted on a site like GitHub, open an issue requesting a license and include a link to this site, or if you’re bold and it’s fairly obvious what license is most appropriate, open a pull request to add a license.
Don’t use the software. Find or create an alternative that is under an open source license.
Negotiate a private license. Bring your lawyer.