In order to create a manifesto or declaration of the "Rights of Man" (or the "Rights of All People") for the twenty-first century, you would first need to determine what rights you want to include in your statement. Historically, such statements have covered such considerations as the right to life and certain freedoms or guarantees to be enjoyed during that life such as freedom of speech, freedom of religion, the assurance of a fair trial if accused of wrongdoing, and so on. In recent years, some statements have felt it necessary to specifically protect freedoms to choose sexual orientation, to protect decisions concerning reproductive rights, or to set out rights concerning protection of private information, among others.
Once you decide which rights you want (or need) to include in your manifesto, you can start thinking about how to present your declarations. Most documents of this sort start by presenting the circumstances that make the statement or declaration necessary. The "Universal Declaration of Human Rights," written in 1948, starts with seven "Whereas" statements of conditions existing at that time that needed to be addressed. It continues
Now, Therefore, The General Assembly proclaims this Universal Declaration of Human Rights as a common standard of achievement for all peoples and all nations,...
The proclamation is followed by the thirty different articles stating specific rights and expectations that the writers of that manifesto felt needed to be stated and explained.
If you follow this type of format, your opening paragraph would become your presentation of the reasons why you feel there needs to be a new declaration of the "Rights of Humanity" under the changed conditions arising in the twenty-first century.