The public voting system is just the same as the jury system. It's only the way that the result is announced that's different.
Let's take the UK public vote as an example. The highest number of votes from the UK public went to Finland, so they were awarded 12 points by us.
The next highest number of votes from UK viewers went to Lithuania, so they got 10 points from us.
From there on, our votes resulted in points being awarded as follows:
Poland 8
Norway 7
Belgium 6
Sweden 5
Ukraine 4
Israel 3
Australia 2
Moldova 1
There were 37 countries participating in the contest. (Those eliminated in the semi-finals still get to vote). The 'Rest of the World' was also permitted to vote this year, meaning that the voting produce a total of 38 sets of results like the one above.
The votes from all of those 38 separate counts are then combined, to produce the totals that are announced on your screen.