AFAIK, all you have to do is go to a US embassy in any country and renounce your citizenship. They'll confiscate your passport and you'll become a
stateless person. You should know that people who renounce their citizenship aren't exactly welcomed back to the US. You may have problems
returning to the US, even for a visit. Being a stateless person has some serious disadvantages, so you might want to think about grabbing citizenship
of some country first, before renouncing the US citizenship.
I don't know whether it is possible to renounce your citizenship while you're still in the US.
Fun fact: Einstein renounced his German citizenship and became a stateless person for a while, before getting Swiss citizenship.


