you can renounce your US citizenship only at the US embassy or consulate in your "other" country of citizenship, for obvious reasons. If you want to be 100% sure that you won't encounter any delays, apply for a "Certificate of Tax Compliance" from the IRS in time before you leave the United States for good.
You have to register with Selective Service once you turn 18. If you leave shortly after your 18th birthday, this will not be an issue.
You cannot become stateless as you cannot renounce your US citizenship unless you are a citizen of another country. If you are not a citizen of the "other" country and they want to get rid of you, they could still deport you to the United States and if you were not a US citizen anymore, the U.S. could not deport you to your country of citizenship as you would have no country of citizenship. Hence, you'd be stuck in the U.S. and that's exactly where the United States doesn't want you to be. So become a citizen of the "other" country first, then you can renounce your US citizenship.
Important to know, once you have renounced your US citizenship, arguably the most desirable citizenship on the face of this planet, you will most likely not be allowed to ever set foot on US soil again in your lifetime. This process cannot be reversed, not even by divine intervention. So say goodbye to family and friends before you leave.
An immigrant from Europe, I live in the charming old mission town San Buenaventura and work as an attorney in Santa Barbara, California.