The new government couldn't levy taxes, so there was no tax policy immediately after the war. Only individual states could levy taxes, which were eaten up pretty quickly by war debt that each state had ($25 million altogether). What the federal government had to rely on was taking out loans to pay off its share of the war debt ($54 million). Now, you don't have to be a financial wizard to understand that taking on more debt to pay off older debt isn't exactly a recipe for success. This was obviously unsustainable.

Things changed after the new Constitution in 1789, especially once Alexander Hamilton got into office. His idea was to impose tariffs on foreign goods to increase American manufactures and make the country less reliant on imports. This worked pretty well not only at increasing industrialization in the US, but it also provided a steady source of revenue.

There were other taxes the US used to generate revenue at this time. The government also levied taxes on alcohol and, weirdly enough, carriages.

The carriage tax was an idea Hamilton had that was sort of like a progressive wealth tax. Each type of carriage had its own tax bracket, so the fancier and more expensive the carriage that someone owned, the more tax they would pay on it. This got Hamilton into trouble when the tax was challenged in Hylton v. United States. The case revolved around whether or not this constituted a 'direct tax' under Article 1, Section 2 of the Constitution. Some hilarious context for this: The delegates at the Constitutional Convention had no idea what they meant when they included the phrase 'direct tax.' In James Madison's journal of the Convention, he wrote this: "Mr. King asked what was the precise meaning of direct taxation? No one answered." However, the court ended up siding with Hamilton that it was not a a direct tax, and it stayed in effect.

All of these taxes were combined with a centralized bank that could issue currency and, most importantly at the time, federalize all the states' war debt and pay it off in full. This policy was quite successful, and kept the US afloat financially through its formative years. If you want a detailed look at those policies and there efficacy, I highly recommend Max Edling's and Mark Kaplanoff's article Alexander Hamilton's Fiscal Reform: Transforming The Structure of Taxation in The Early Republic.

Of course, not everything was sunshine and roses. That alcohol tax I mentioned fell disproportionately on frontier whiskey distillers, who relied on whiskey because it was easy to transport to market over long distances. This resulted in the Whiskey rebellion during Washington's presidency. And one of the most ironic things about this whole time period is that arguably Americans were now paying even more in taxes than they had under the British.

Anyways, tax policy isn't my specialty, but I hope I was able to give some useful context nonetheless.

EDIT: Punctuation