On the map (right), you will see lines between countries who have a history of voting for each other, for example the United Kingdom and Ireland, Cyprus and Greece, and Turkey and Azerbaijan.
Usually the countries in a bloc, such as the Balkans, the Nordics, the former Soviet Union and Former Yugoslavia, will vote for each other as they are neighbors and want to stay on good political terms with each other.
Sometimes this is not the case, as the 2014 annexation of Crimea from Ukraine by Russia made many think that Russia weren't going to receive as much points in the 2014 contest. However, Ukraine and Russia exchanged points, and both countries had a top 10 placing. Ukraine is a former USSR country, and so will probably give Russia points, anyway.
In the televoting era of the contest, people who live in a country outside their place of origin will often vote for the song of the country they originally came from (i.e.: Lithuanian people in the United Kingdom voting for the Lithuanian song, etc.). A prime example of this is Poland's 2016 entry, which placed third in the grand final televote with 222 points despite being second-last with the jury with only 7 points. Many believe that this is because of the massive Polish diaspora across Europe voting in big numbers for it.