I have done it twice in my lifetime. The rules are different in different countries. YES, you need a passport to even get on a plane to a foreign country and sometime you need to apply for a visitors visa just so you can visit and the time is limited, depending on the country. Usually it is 3 months or 6 months and you have to sign a paper saying you have enough money to support yourself during that time and will not try to find employment. When you in the country, on a visitors visa, usually you are not allowed to apply for residency during that time. If you decide, gee, this is a nice place, you have to go home and apply from your home country for residency of some sort. It can be that you got engaged while you were there visiting, (here in Norway, an engagement only gives you 6 months to stay) Getting married to a citizen usually helps, if you are willing to go down that road. Being independently wealthy also helps or having a multi-million dollar company you want to move to that country with.
I also have friends that frequently move from country to country because of their jobs. Norwegians in Singapore, Brits in Texas. They are able to do this because the International Corporation they work for assists. (as for the Brits, there was one problem. They had lived together as a common-law husband and wife for 15 years all over the world. He got the promotion to Houston and they had to get married, or else she wouldn’t qualify to reside in Texas.)
I became a permanent resident in New Zealand because the rules were a bit more relaxed back in 1988, when unemployment wasn’t such a problem. They actually had a list of professions they were trying to recruit from over seas. I think they still have a similar list. and I had a family sponsoring me, so I had a place to stay and meals in my tummy. After a rather gruelling 3 months, I got a job. Not the one I was after, but it got my residency and I lived there for 15 years and I can go back and live there when ever I choose. I changed jobs a few times. Never had trouble finding work. Getting my drivers license was inexpensive and relatively simple, and the culture agreed with me perfectly.
I ended up in Norway because I married a guy I was head over heals in love with, but even then, if we had broken up during the first 3 years of our marriage, I would have been booted out of the country. PermRes comes only after the 3rd year of marriage and on the anniversary of your paperwork, the two of you have to go together to the police station and state that you are still together, you pay a crazy amount of money, they take your passport (just the foreign one) and you may or may not get in back in the mail for 6 months. They make sure you are belittled and shamed and made to feel less than. So, I don’t recommend marriage to get into a country, even if you think you are in love.
First, get a passport. Then, do some travelling. If you still think the grass is greener, pick a country. Usually the countries have a website dedicated for exactly this sort of thing. Here is New Zealand’s http://www.immigration.govt.nz/ Here is Australia. http://www.immi.gov.au/
It is always a bit more complicated than you think.