If someone were paying a bill or for a debt in 1790, did they pay with cash or a note of some sort?
It varied from one place to another. Some of the common possibilities:
In relatively civilized areas with good access to British commerce, like Boston, New York and Philadelphia prices and rents were often denominated in terms of the penny sterling.
In farming areas bushels of wheat were commonly used to pay rents and bills
Privately coined "tokens" were very common due to the scarcity of British silver and there are about a hundred or so well-known tokens; a typical example was the Kentucky token (see photo below); these tended to be used for smaller bills, not large payments
In many areas, especially the south and midatlantic, Spanish milled dollars were widely used; our term "dollar" comes from this coin, which was a reale; for larger commercial transactions the gold Spanish doubloon (32 reales) was a standard of money
Private banks issued "bills of credit" and "promissory notes" which often circulated as a paper form of money
The Continental Congress issued large amounts of bills as a paper money denominated in Spanish dollars and these circulated widely, often at a heavy discount
The individual states had each originally issued a lot of paper money, but by 1790 most of these bills were worth less even than Continentals and the Constitution, enacted in 1789, made them illegal to produce so they were dying out; nevertheless they were still in use
The Kentucky Token