If a citizen owned a slave, he or she could free him / her. The Wikipedia article gives some reasons for doing this:
Slaves were freed for a variety of reasons; for a particularly good deed toward the slave's owner, or out of friendship or respect. Sometimes, a slave who had enough money could buy his freedom and the freedom of a fellow slave, frequently a spouse. However, few slaves had enough money to do so, and many slaves were not allowed to hold money. Slaves were also freed through testamentary manumission, by a provision in an owner's will at his death. Augustus restricted such manumissions to at most a hundred slaves, and fewer in a small household.
The later paragraph suggests it was later very common practice:
Already educated or experienced slaves were freed the most often. Eventually the practice became so common that Augustus decreed that no Roman slave could be freed before age 30.
It seems that "Augustus" means Octavian August and it would mean that this was quite widespread before Christianity, if it became a danger to state economy.
Do we have some sources confirming it was a widespread practice? How many slaves yearly were freed? (the text from Wikipedia does not cite any sources)
PS. I understand that there were many types of work, and they who worked in mines, galleys etc. were freed less frequently than those who were writers, baby-sitters etc.