Relentless advertising the week before the election. Any sooner than that and you're wasting money. The electorate has the collective memory of a goldfish so wait until the few days, and especially the weekend, before the election and dump it all into an overwhelming advertising campaign. Every other commercial that comes on TV should be one of your attack ads listing everything horrible the candidate you oppose has ever done wrong.
Buying politicians won't work, that kind of money will either buy one for a few years or many for a few months. But $500m is less than a million dollars a year for just the house of representatives and when that money dries up their normal donors will be there with big fat checks ready to change policies back to the way they were before.
In order to enact real change you'll need to actually replace the people in power. And even then the major sticking point is making sure that the candidates you endorse actually make the changes that would limit future corruption.