Please note that "Yibbum" is the Hebrew term for "Levirate Marriage."
How
Completing the marriage "transaction" via intercourse: Kiddushin 2a, 4b [2x], 5a, 5b, 9b, 13b-14a
The youngest age at which the Above works: Kiddushin 10a
Whether the marriage can be transacted via exchange of money or a legal bill: Kiddushin 4b [2x], 9b, 14a
Whether her acquiescence is necessary for the transaction: Kiddushin 5a, 5b, 14a
Problems
If one of the males eligible for Yibbum, engages her sister before Yibbum is done: Megillah 18b
If the Woman claims, during the first 30 days, that the Brother-in-Law has not had sexual relations with her: Yevamot 111b, 111b-112a
If the Woman claims, after the first 30 days, that the Brother-in-Law has not had sexual relations with her: Yevamot 111b, 111b-112a
Above two cases, where he admits that she is telling the truth: Yevamot 111b, 111b-112a
If she says there were sexual relations, and He denies it: Yevamot 112a
The former co-wife of a woman who did Yibbum and now claims that there were no sexual relations: Yevamot 112a
Bringing an asham taluy offering for possible guilt, and divorcing due to possible incest, if a childless widow marries her brother-in-law for yibbum [levirate marriage] within three months of her first husband's death, and then has a child seven months after her re-marriage: Keritot 17b-18a