While this of course depends on exactly where you end up moving to, and you should check the specifics there, I can say that near to everywhere seems to have pretty much the same systems in place: 5 years legal residency enables one to apply for permanent residency/citizenship after passing a series of tests, usually basic language proficiency alongside laws/culture/history of wherever you're migrating to.

Until that point you'll usually have to do something like check in with immigration once a year, dependent upon what visa (work, education, tourist, etc) that you end up on. But like another poster said, you don't really need to worry about most of this to begin with, as at most places you'll be granted a visa on arrival that'll be good for more than enough time to find a job. The most you might want to do is drop by the embassy of wherever you plant to go to. They can give you more information, and also set you up with a visa that will generally last much longer than the visa-on-arrival if desired.