Did they have a checkbook type of thing for credit or have the bank or someone be a witness?
Many people in the 19th and 20th centuries in rural North America got credit from their local shopkeeper, who they knew personally, who knew where they lived, knew their families, etc. These shopkeepers often got paid in goods (eggs, butter, produce..) rather than cash. The shopkeepers would keep an account of what had been paid and what was owing. Sometimes people would deed land to the shopkeeper in order to pay off a debt.
People could also ask for someone to stand surety for a debt. There's an anecdote from early 20th century Nova Scotia about two young fellows who went to buy themselves new wagons. The wagon maker asked them if their fathers would stand surety for the debt. The first young fellow said, yes, his father would pay if he couldn't. The second young fellow - whose father was notorious for not paying his debts - said, if I don't pay you, you'll never see the money. The wagon maker knew both of their fathers and knew they were both telling the truth, so they both got the wagons.
In rural areas personal reputation was hugely important.