Winona Kirk was the wife of George Samuel Kirk Sr., and the mother of George Samuel Kirk Jr. and James T. Kirk. She was born in 2210 and was of Sioux decent. (TOS novels: Best Destiny & Final Frontier; comic: "Who's Who in Star Trek").
She met George Samuel Kirk in the late 2220s and the two were soon married. In deference to George's support for the Back to Earthers movement, they became farmers in the small town of Riverside, Iowa. Despite George's support of the Back to Earther's movement, he still served in Starfleet as a security officer and was away from Earth for long periods. (TOS novel: Final Frontier).
Despite this the Kirks' still managed to start a family with George Samuel Kirk Jr., their eldest son, being born 12 August 2231. On 22 March 2233, James T. Kirk, their youngest son, was born early when Winona accidentally tripped over one of the pigs located on the farm. (ENT novel: Last Full Measure; TOS novel: Enterprise: The First Adventure).
When her sons were young, Winona tried to instill many of her core values into their minds, including the view that taking part in a race was more important that winning it. However, young James didn't share his mothers view. (TOS novel: The Great Starship Race).
In the Crucible continuity, both Winona and George died while James was at a young age, and he was sent to reside on Tarsus IV. However, this doesn't fit into the main novel continuity, which has Winona live well into the 2280s.
In 2247, Winona and her children left Earth to accompany George on his assignment to the planet Grex following the Orion withdrawal from the planet. Unfortunately, a year later, the family were forced to leave Grex aboard the transport vessel, Eliza Mae, when a civil war broke out between the native factions on the planet. They presumably returned to the family farm in Riverside. (TOS novel: The Janus Gate: "Past Prologue").
In late 2249, Winona and the boys traveled to see George off as he prepared to leave for an assignment on the planet Hellspawn. During the goodbye, James insulted her father, which led to Winona slapping him hard once George had left. (TOS short story: "First Star I See Tonight"; novels: First Frontier & Crisis on Centaurus).
Following the death of her husband, Winona left Earth in 2259, to stay with her eldest son and his family on Deneva. In 2264, Winona and her eldest son attended the change of command ceremony of the USS Enterprise (NCC-1701) from Captain Christopher Pike to James T. Kirk. (TOS novels: Enterprise: The First Adventure and Final Frontier).
Around 2266, Winona decided to return to the family farm on Earth and cared for the Kirk farm alone for seventeen years. In 2269, a fire at the broke out and she was injured as a result, although fortunately she wasn't killed. However, a second fire broke out on 2 June, 2283 and Winona sadly died later that day as a result of pneumonia, which was caused by smoke inhalation. As per her wishes, she was cremated and her ashes were placed in a wall crypt in a chapel that stood in Riverside. (TOS short story: "First Star I See Tonight"; novel: Time for Yesterday).