Atticus Finch refused to deny a client services just because he or she could not afford to pay him with money.  Mr. Cunningham was one such client.  One night, after meeting over a legal matter, Mr. Cunningham said to Atticus, "'I don’t know when I’ll ever be able to pay you.'"  Atticus reassured him that was okay and told him not to worry.  After the man left, Scout "asked Atticus if Mr. Cunningham would ever pay."  Atticus assured her that he would, but not in the way other people usually paid.  "'Not in money,' Atticus said, "'but before the year’s out I’ll have been paid. You watch.'"  Scout soon witnessed that Atticus was right:

"One morning Jem and [Scout] found a load of stovewood in the back yard. Later, a sack of hickory nuts appeared on the back steps. With Christmas came a crate of smilax and holly. That spring when [they] found a crokersack full of turnip greens, Atticus said Mr. Cunningham had more than paid him."

After the delivery of all these goods, Scout asked her father why Mr. Cunningham paid him in such a way.  Atticus told her that it was "'the only way he [could] pay'" because Mr. Cunningham "'[had] no money.'"  He also told her that Dr. Reynolds "'[charged] some folks a bushel of potatoes for delivery of a baby.'"  Atticus told Scout that cash was hard to come by in Maycomb County.  The farmers could not afford to pay cash to the professional people because all the money they had went toward mortgage interest on their land.

Scout tried to explain the way things worked to her teacher, Miss Caroline.  She told her teacher that

"'the Cunninghams never took anything they can’t pay back—no church baskets and no scrip stamps. They never took anything off of anybody, they get along on what they have.'"

Despite their poverty, people like the Cunninghams had a sense of pride.  They did not want to be indebted to anyone.  That was why they paid what they could.  Atticus respected that.  He gave them a sense of dignity by accepting their food and firewood as if those items were as good as cash.

They pay for services through goods and services they can provide when they don't have the cash to do so.  During the setting of the novel, The Depression, it was fairly common practice for professionals such as doctors and lawyers to provide for much needed services in this way.  It was an act of charity, but it perserved the honor of the client relationship and did put food on the table, or wood in the fireplace.

In this novel, Atticus explains this to Scout in an effort to teach her the different ways that people "do right by each other."  Atticus helps Cunningham with his entailment legalties, and in return, the Cunninghams bring foodstuffs -- he accepts these donations with as much honor and respect he would traditional payment, and even compliments them on the quality of the product.

How do the Cunninghams pay their bills in Harper Lee's To Kill a Mockingbird?

In Harper Lee's To Kill a Mockingbird, the Cunninghams, along with many other people in Maycomb, struggle financially—especially in light of the Stock Market Crash of 1929 which hit the poor the hardest, especially those in the South still attempting to recover from the ravages of the Civil War, which had only ended some sixty-five years earlier.

Atticus provides Mr. Walter Cunningham with legal assistance but Walter cannot pay for it. He pays, instead, with goods, in the old-fashioned way of bartering: goods in exchange for services. Mr. Cunningham is a proud man, and Atticus is aware of this and has no desire to make Cunningham feel embarrassed that he hasn't the cash. Atticus is very serious in his gratitude when the other man stops by to settle his "account."

Specifically, we read in Chapter Two:

One morning Jem and I found a load of stovewood in the back yard. Later, a sack of hickory nuts appeared on the back steps. With Christmas came a crate of smilax and holly. That spring when we found a crokersack full of turnip greens, Atticus said Mr. Cunningham had more than paid him.