A player can only be a member of the national team of his own country, he will also never be able to change his nationality.
There are two national teams: the national teams with players of all ages and the U-20 national teams with players that are younger than 21 years and one day.
The skill level required for a player to make it into the national team differ from country to country. A player typically needs to have higher skills and form than other nominees, in order to make it.
U-20 National Team
U-20 National Teams consist only of players below 21 years of age from (born in) the national team's country. In most countries, only the players that are pulled as 17 year olds with decent primary and secondary skills stand a chance to be trained to a high enough level to be selected before they turn 21.
In large countries, this often means only players who are aged 17, pulled shortly after their birthday, with an excellent main skill and an appropriately-timed birthday are suitable U20 material. As such players are highly prized, they are often sold for incredibly high prices.
The national coach and U-20 national coach are elected every two seasons by the users of the country the team is from. National coach selects National team trainer and players and eventually a staff of users that can help him.
Note that NT trainer is a different figure: he is a player converted to trainer in a club, he is important only for Leadership and he doesn't keep form high. Another differnce is that trainer must have the same nationality of the NT, while can be elected as coach every user in the HT world.
The senior team's national coach is elected every two seasons by the users of the country the team is from; the election is staggered to happen on different seasons than the U-20 elections. It starts the day after the World Cup final (usally at 7:00 AM Hattrick Time) and lasts for a week.
Having a national team player is considered an honour. Many teams around the globe fully dedicate their teams to training U20 and/or NT players.
On the players page of their club they are accompanied by a flag of their country. Furthermore the page of the specific player mentions the following: "Also part of Team ...!"
Players gain experience by playing in national team matches. As well, a national team player will earn a salary reduction, when playing in a national team match, of 33-40% depending on whether or not he is playing in his home country.
Most teams use a database to keep track of their players. There usually is a tracking tool that has been granted the status of a global tracker and that any country can use if they want to.
Besides it, there are a few local trackers that were created by users that maintain a CHPP licence for a particular country.