Round 1
1->5
2->6
3->7
4->8
Round 2
1->3
2->4
5->7
6->8
7, 8 - lost twice and are eliminated
Round 3
1->2
3->5
4->6
5, 6 - lost twice and are eliminated
Round 4
1->4 (since they already played against #3)
2->3
3, 4 - lost twice and are eliminated
Final
1->2 for the tournament win
3->4 for third place
More details http://ru.wikipedia.org/wiki/Олимпийская_система_с_выбыванием_после_двух_поражений
PS I prefer a simple Olympic system.