You can’t. That’s not enough money.

Make the lives of your community better instead.

You’d start by attending $10,000 plate dinners, and shaking hands with candidates and expressing views. Hire a few $60k a year idealists for a think tank to publish papers. Pick 1-2 issues and hammer them. Pay lobbyists to set up meeting and propose/write legislation and amendments.

As some of your (hopefully idealistic) candidates win, you ask them to help drive your issues through. Get them to make concessions to other people’s proposals for support on theirs, helped by your lobbyists. Use your think tank to drove issues and provide talking points and legislation.

That’s the traditional view. A better approach might be to create a 501c3 and run positive message ads that give you a warm feeling about america in general, say nothing of substance, and include a candidate you like’s name sometimes. Then another pac showing pictures of the candidate you don’t like and chanting “hate hate hate” behind them. Play to your audience.

Hire a couple people who are really good at making memes and other easy to digest content relative to your cause, then hire 1000 3rd world workers to constantly spam that content on the 10 biggest social media outlets, chat boards, etc. being sure to hit all the big groups that are in the ballpark of your cause. Amplify existing messages favorable to your cause with reposts and reactions.

Basically just a big astroturfing campaign.

My first move is to think about safety and longevity. I’m going to need a private island as a base of operations. Caution also dictates having a few backup homes, so my enemies never really know where I am. Beyond that, I need to spread my message, so I’m going to need a private plane. Something modest and a few years old is fine. This is a charitable effort. It isn’t about me. And in the name of charity and effectiveness, let’s go ahead and add a boat on there, too. Now, to really clear our heads before we get going and make sure we’re enacting the right policies, we’re going to want to bring in some girls…

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.