A player blamed others. Then I reported, what would happen to him or her.

Click on every "new" post you see in this sub-boards and tell me what Riot does to them.

They would need a decent amount of reports against them from other people for Riot to take action. Sadly, Riot can't fix the personal issues of toxic people and their inability to dispose of their ego's; but they have implemented a mute button that will temporarily terminate you seeing them talk in chat (in game), and they also don't have a good way of blocking people yet. I believe you have to befriend that person in order to block them.