How has the government tried to make paying for campaigns more fair?

If you're referring to regulations:

There is a maximum amount of money individuals and organizations can send directly to candidates (HARD MONEY)

A way to bypass this is if you send money to a political party which then runs ads for campaigns

Example; You already contributed your maximum $5,000 to the Trump Campaign but you want to contribute $20,000 in total so you give the Republican Party $15,000.

Also no foreign money is allowed in political elections.