Generally speaking, a Yartzeit the anniversary of a family member's passing, on which several practices are observed in memory of the deceased takes place on the calendar date on which the deceased family member had passed away. Thus, for example, if a person died, Heaven forbid, on the first day of the month of Tevet, his family members observe the Yartzeit every year thereafter on the first of Tevet.
An exception to this rule is a case where the first year after the family member's passing is a leap year, meaning, it contains two months of Adar (Adar Alef and Adar Bet). The first Yartzeit after an individual's passing is observed twelve months after the death, which, during a leap year, occurs one month before the calendar date. For example, if a person passed away on the first of Tevet during a leap year, the first Yartzeit will be observed twelve months later on the first of Kislev. Given the addition of a second Adar, the Yartzeit will be observed in Kislev, rather than in Tevet. In all subsequent years, however, the Yartzeit is observed on the calendar date, the first of Tevet. This is the ruling of Rav Shemuel Pinhasi (contemporary, Israel), in his work Haim Va'hesed (p. 343; listen to audio recording for precise citation).
Summary: A Yartzeit is observed on the calendar date of a family member's passing; however, the first Yartzeit is observed twelve months after the passing, and thus if the first year is a leap year, the first Yartzeit will be observed exactly one month before the calendar date of the passing.
