First, people would have to vote an EU-sceptic majority for their domestic parliaments. This would need to happen in a majority of EU countries. Then this majority of EU-sceptic governments could achieve a majority either in the Council or in the Commission, and propose laws to change the EU governance. Then the Parliament would have to accept these laws.

I think it would have to be the Council, it's difficult to see the Commission proposing a law that decreases the power of the Commission.