Currently, if you want to become an astronaut for a traditional space agency (i.e. NASA, ESA, Roscosmos) you basically need to be a citizen of that country or in ESA's case, a citizen of one of the ESA Member States.
In the USA, the most reliable method of becoming a NASA astronaut is to be a military test pilot and eventually cross over to NASA. If you want to apply as a flight engineer or scientist, you need to be very lucky and distinguish yourself in your field somehow.
Realistically, if you want to be a space agency sponsored astronaut, you need to be extremely lucky, dedicated, and skilled. Setting your career goal as "become an astronaut" isn't a wise move as it's setting yourself up for failure.
The easiest way to become an astronaut today is to become rich. It's a pretty safe bet to say that in 20 years, space tourism will be far bigger than today and even now, if you've got a couple dozen million dollars laying about, it's doable.