A resposta terá que ser dos livros, já que o programa não tem informações a esse respeito, tanto quanto eu sei.

Primeira coisa, há vários relatos sobre seu desempenho anterior. Tyrion diz que Littlefinger aumentou três vezes as receitas de Gulltown e que foram as receitas da Coroa que foram multiplicadas por dez. Lysa Arryn diz que aumentou dez vezes a receita de Gulltown.

Ten years ago, Jon Arryn had given him a minor sinecure in customs, where Lord Petyr had soon distinguished himself by bringing in three times as much as any of the king's other collectors. King Robert had been a prodigious spender. A man like Petyr Baelish, who had a gift for rubbing two golden dragons together to breed a third, was invaluable to his Hand. Littlefinger's rise had been arrow-swift. Within three years of his coming to court, he was master of coin and a member of the small council, and today the crown's revenues were ten times what they had been under his beleaguered predecessor . . . though the crown's debts had grown vast as well. A master juggler was Petyr Baelish.
_{ACOK - Tyrion VI}

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My father said he was too lowborn, but I knew how high he’d rise. Jon gave him the customs for Gulltown to please me, but when he increased the incomes tenfold my lord husband saw how clever he was and gave him other appointments
_{ASOS - Sansa VI}

Eu diria que ele usou os mesmos truques que usou quando era o mestre da moeda, se essa performance é construída e aperfeiçoada a partir de seu modo anterior de fazer os dragões se reproduzirem.

Ele não acreditava em colocar ouro em um cofre e trancá-lo. Ele costumava investir as receitas em empreendimentos para gerar mais receita. Além disso, ele era ótimo em escolher os homens certos para o trabalho certo, o que aumentava a eficiência da burocracia e, portanto, as receitas. Ele não se importava com o nascimento de um homem desde que estivesse em condições de fazer o trabalho. E quase sempre, esses homens provaram ser mais qualificados do que seus equivalentes mais velhos.

Oh, he was clever. He did not simply collect the gold and lock it in a treasure vault, no. He paid the king's debts in promises, and put the king's gold to work. He bought wagons, shops, ships, houses. He bought grain when it was plentiful and sold bread when it was scarce. He bought wool from the north and linen from the south and lace from Lys, stored it, moved it, dyed it, sold it. The golden dragons bred and multiplied, and Littlefinger lent them out and brought them home with hatchlings.

And in the process, he moved his own men into place. The Keepers of the Keys were his, all four. The King's Counter and the King's Scales were men he'd named. The officers in charge of all three mints. Harbormasters, tax farmers, customs sergeants, wool factors, toll collectors, pursers, wine factors; nine of every ten belonged to Littlefinger. They were men of middling birth, by and large; merchants' sons, lesser lordlings, sometimes even foreigners, but judging from their results, far more able than their highborn predecessors.
_{ACOK - Tyrion VI}

Não sabemos

Os livros só têm a seguinte passagem sobre como ele fez isso e visto que Petyr sempre age em segundo plano é sensato assumir que seus métodos não são conhecidos.

Petyr's breath is always fresh . . . he was the first man I ever kissed, you know. My father said he was too lowborn, but I knew how high he'd rise. Jon gave him the customs for Gulltown to please me, but when he increased the incomes tenfold my lord husband saw how clever he was and gave him other appointments, even brought him to King's Landing to be master of coin.
_{A Storm of Swords, Sansa VI}

There are several branches of House Arryn scattered across the Vale, all as proud as they are penurious, save for the Gulltown Arryns, who had the rare good sense to marry merchants. They're rich, but less than couth, so no one talks about them.
_{A Feast for Crows, Alayne II}