I want out

I want out of the US. My dream home is either New Zealand or Australia.

My question is: if I have an enough for a one way ticket and enough for a hotel/place to stay, is it that simple to leave and become a citizen?

I had a friend tell me you can just show up, go to an embassy, apply for a temporary visa, get a job, then apply for a work visa, and eventually work towards citizenship.

Is this true?

Edit: being told is not the case. How do I get out of here and where can I go?