A sovereign is effectively a governmental entity. The United States is a sovereign entity, as are individual states, and the Indian tribes. Royalty are technically sovereigns, although for many countries they are merely representative of the sovereign government. In any event, being sovereign is not something you declare. It is simply being recognized as such by other sovereigns, courts, etc.
A United States National is a non-citizen who has almost all the rights of a U.S. citizen. The exact law can be found here: http://www.law.cornell.edu/uscode/8/1408.html. The short version is that if you're born in (effectively) American Samoa, or are the child of U.S. Nationals, you are a National. You are also a National anyway if you are a citizen, as a citizen has all the powers of a U.S. National plus the ability to vote in federal elections.
You may be talking to people who are trying to find loopholes to avoid paying taxes by revoking their citizenship or social security numbers. This is usually a scam, and always illegal.
Your goal of living off the land is commendable. Alaska has an interesting subsistence program that even non-Alaskan Natives can participate in. Living that lifestyle can certainly reduce your tax bill. But don't forget, even the Amish travel on roads built by the government.
As a U.S. Citizen you do have other obligations. You must be counted for the Census. If you're a male you must register for the Selective Service once you turn 18. In short, you remain beholden to United States law.
There is a way to renunciate your citizenship. The exact information can be found here: http://travel.state.gov/law/citizenship/citizenship_776.html but in brief, you must be in a foreign country with an American Embassy and give an unequivocal written statement about your intent to revoke your citizenship. Have another country willing to take you in beforehand, as being without any citizenship can have serious consequences on your ability to travel, establish bank accounts, etc. It's a significant decision.
If and until you and I sign an Agreement for Legal Services, I am not your attorney. These answers are provided for informational and/or novelty purposes.