What conditions does a society need before it can successfully implement fiat currency?

Law.

A decree that cites that the fiat money being issued is legal tender for exchange and settlement of debt between two parties.

When the first fiat was issued, it was asset backed, which at the time was gold, silver, etc. (precious metals), but because it was the first time money was being issued, it was hacked (taken advantage of), a lot. Gold and Silver was stripped from the coins. Coins were remelted and the melted ore was sold, etc. The basic law to settle was first introduced and then defacing or melting of coins law was introduced.

But those were all teething problems. The basic premise was the law, that was behind the money that allowed debts to be settled using it.