At the end of the season, you can register to be elected. You can only register for 1 country. Then people have a vote, whoever has the most votes gets the job. Anyone can apply.
To locate your coach, change your menu (on the right) to long menu. And it should list your country, national teams, and stuff like rankings, election etc in 1 category. Click on National Team to visit your national team's page where it shows you the coach.