The first thing that you must do is find a country that you wish to live in and begin looking at the economic factors in that country. Just because you have romanticized ideas of what a country is like does not mean that these ideas are true. For example, many South American countries that have been traditionally poor are undergoing record growth, while many traditionally rich European countries are currently going through an economic downturn. You must learn how a country is currently doing economically because if the economy is flourishing, you will have a better chance of getting hired.
You must also consider social factors, as this will greatly influence your decision. You would not want to go to a country with an extremely low standard of living, as your end goal would be to make enough money to live comfortably. Therefore, you will want to avoid certain areas of the world where the standard of living will be much lower than what you are used to. The health care that you will receive is also a major factor because jobs in construction are inherently dangerous and if you are injured, you will want to make sure that you are taken care of.
It is also very important to visit a country before agreeing to work there, which will give you a clear view of what it will be like to live there. When you visit, make sure that you do not simply stick to the tourist areas, but actually explore the city that you have chosen and get a good idea of what everyday life is like. This will definitely help you to make a decision and while you are wandering around the city, you can even begin looking for construction manager jobs. It also would not hurt to have a resume with you at this point, just in case you run into someone who can help you get one of these jobs.
Make sure that you return home in order to get everything together before you make this move and remember that your entire life with chance if you take one of these construction manager jobs. Also keep in mind that the jobs in construction in other countries might be done a different way, so keep an open mind and do not be afraid to return home if things are not going your way.