What are the requirements to being a UN or U.S. ambassador?

I am not either of those things, but I can give you some general guidance. Hopefully someone else can give you more specific advice.

There are plenty of people who work for the UN, or work at the UN on behalf of the US. These jobs are highly sought after and are tough to get. The single most important thing you can do is have top grades in school. Beyond that, you need to have a global focus. It would probably be wise to major in something like International Relations or Political Science, but more importantly, you need to be 'involved.' Most colleges will have various programs that have an international focus. Don't just join those programs, lead them. If there aren't enough groups to join, or you want to do something different, start your own organization and make it into something huge that people will notice.

When you are in school, and when you get out, networking is key. Lots of US ambassador jobs are given as favors. Sad but true. Being involved in US politics is important if you want the politicians who give these jobs to people to notice you. If you want to stay out of politics itself, then be involved tangentially. Work for global non-profit organizations or charities, or work for policy think tanks, anything that is going to put you in contact both with politicians as well as leading academics in the spheres of public/foreign policy and international relations.

Also, learn a few languages. One way to start working at the UN is as an interpreter. But also learn about other countries, and if you can, specialize in a few. Condoleeza Rice was an expert on the Soviet Union, and her academic work on the USSR is what got her noticed by the politicians who then appointed her to various positions. Susan Rice, Obama's current National Security adviser and former UN ambassador wrote her dissertation on Zimbabwe and you could generally say her specialty was Africa during the Clinton administration. John Bolton, Bush's UN ambassador, by contrast, was a lawyer who got into politics first, international affairs later.