(covers information from several alternate timelines)
Parenting was the set of skills and methods used in the practice of raising children, which fell within the medical science study of pediatrics.
When Data created his "daughter" Lal, in 2366, he understood parenting to be "the consequences of creating a new life," and as such, took it upon himself to prepare for Lal's upbringing by scanned all available literature on parenting, which he noted was confusing subject. He stated that "One traditional doctrine insists, "Spare the rod, spoil the child," suggesting a punitive approach. While a more liberal attitude allows a child great freedom." Data also learned that Klingon parenting seemingly contradicted both doctrines.
Later, when Starfleet wished to take Lal from Data, he explained that he could not give up his child, because "It would violate every lesson I have learned about Human parenting." He felt that since he "brought a new life into this world," it was "[his] duty, not Starfleet's, to guide her through these difficult steps to maturity, to support her as she learns, to prepare her to be a contributing member of society." (TNG: "The Offspring")
When Kes underwent a premature elogium in 2371, she briefly considered becoming a parent with Neelix, with whom she was at that time romantically involved. However, she questioned her own ability to be a mother, wondering how she could provide proper guidance to a child when she was still essentially a child herself. Neelix had never previously considered becoming a father and was thus initially hesitant to take Kes up on her offer; however, after consulting with Tuvok, who related to him his own experiences as a parent, Neelix eventually changed his mind. By this time, however, Kes had decided not to conceive, though she promised Neelix that they might have another chance if he were willing to wait (however, Kes terminated their relationship long before this time). (VOY: "Elogium")
In an alternate timeline, Kes did eventually become a parent, bearing a child with Tom Paris sometime around 2375. This child went on to marry Harry Kim, bearing a child of her own with him around 2378. (VOY: "Before and After")
When The Doctor created his own holographic family in late 2373, which B'Elanna Torres later "tweaked" to make more "real", he utilized information in intended to use his personal database on "pediatric care and childhood development" to assist him in preparing for potential parenting problems.
As a result, he decided to set some parameters for his children, which he explained to them was part of "good parenting." These parameters, which he described as "limits" or "boundaries", were outlined in his revised family schedule and his list of family rules and regulations. (VOY: "Real Life")
In 2377, upon learning his wife B'Elanna was pregnant, Tom Paris, facing the responsibility of raising a baby, sought counsel on parenting from Tuvok as the only crewmember aboard USS Voyager who had experienced fatherhood. Tuvok, who felt his parenting skills were somewhat dormant as it had been many years since his children were young, was able to offer that "offspring can be disturbingly illogical, yet profoundly fulfilling. You should anticipate paradox."
Likewise, in anticipation of Torres' pregnancy, The Doctor developed a parenting class especially for Paris and Torres based on the expansion of his personal database in obstetrics and pediatrics. Among the areas The Doctor planned to explore in his parenting class were birthing techniques, feeding options, and bonding strategies. (VOY: "Lineage")