They had one hymnal. Calpurnia's son, Zeebo (the town trash collector), was taught to read by his mother, and he uses the call and response technique. He'll sing a line or two from the hymnal, and the congregation repeats it. This episode in the novel highlights many important elements, not the least of which is what the children learn about Cal. That her son is literate is important. In addition, they get a first hand sense of the scale of poverty within the town.
Many hymns were sung using "call and response". In this type of singing, the choir leader and the choir sing a line of a song aloud and then the church congregation sings it back to them.
Also, most hymns are passed on from generation to generation, so it is also very likely that the congregation had the songs memorized because they grew up listening to them over the years.
During the service, Reverend Sykes called on Calpurnia's eldest son, as the music superintendent, to lead the congregation into the singing of the first hymn. Since there were no hymn books, Zeebo, who had been taught how to read by his mother, first announced the hymn number and then read its opening line. The congregation would then sing the line and Zeebo would then read the next one, and they would sing and so on, until it came to the chorus, when he would close the battered hymn book as a signal for the congregation to continue singing without his lead. He would only lead them when he read the last line of the hymn as an indication that that was its end.
It is clear that this method had become custom for the text indicates that where Zeebo did not read the line too clearly, the congregation would wait for him to repeat it. It is also evident that the congregation knew the tunes by heart but probably did not know some of the verses in a few of the hymns. There must have been some popular ones which, obviously, would have been sung with gusto.
As it was, First Purchase Methodist Church was poor and so was its congregation and it could, therefore, not afford buying hymn books. Secondly, as Calpurnia told Scout later, only four of the black people in the Quarter could read, including her and Zeebo, which would have made the purchase of hymn books a futile exercise anyway. It is clear, though, that the congregation was coping quite well with Zeebo leading them.
The congregation did not have the funds to purchase the hymn-books that would be needed. As with tradition the songs have been passed down orally. Songs would change from written form and take on characteristics unique to an area.