I am interested on the best practices in European countries such as Estonia, Latvia, Slovenia, Ireland, Luxembourg, Croatia, etc., and similar practices (if any) in the countries of South America and Southeast Asia.
Dear Afrim, although several countries allow their citizens who live abroad to cast their vote, in some of them it is possible to participate only in presidential elections not in the legislative ones. In those cases in which citizens can elect representatives to the National Congress (such as El Salvador or Honduras) they have an electoral district (an international one) in addition to the national ones, in which voters can choose a representative of the population who live abroad. So, candidates run and compete for that seat. I suggest you to do some research about these cases and other similar ones. Let me know if this helps.
the Croatian diaspora is enabled a right to vote in the presidential and parliamentary elections. This is regulated by the Constitution of Croatia. The country must organise polling places, usually in embassies.
The diaspora also has a say in a referendum, although when collecting signatures for a referendum (10% of all eligible voters is required to carry out a referendum) the referendum campaign group doesn't collect outside of Croatia, mostly because it is not sure how this should be conducted.
Voting in Luxembourg is compulsory. A voter who fails to vote can be punished by a fine ranging from 100 to 250 euros, the first time and 500 to 1000 euros the second time.
Voting by post is mandated to those who have their residence abroad.