When Tisha B’Av falls on Shabbos/Sunday, when and how should someone who will not be fasting hear Havdalah?
One who will not be fasting, whether a man or a woman, must hear Havdalah on Motzaei Shabbos before eating or drinking. A child may eat and wait with Havdalah till Motzaei Tisha B’av.
If there is a male child (who has reached the age of chinuch etc.) present, havdalah should be made on wine (or grape juice) and the cup is given to the child to drink, as is customary during the nine days. If a woman made Havdalah, the wine must be given to a female child. If there is no child present, havdalah should be recited over chamar medinah, such as beer, coffee or tea.
A woman who is not fasting may ask her husband to recite havdalah for her although he is fasting. In that case, he will have also fulfilled his own obligation to recite havdalah (and will thus not need to repeat it on Sunday night). The wine should in this case be given to a male child. (It is important to note that a man cannot fulfill his obligation of havdalah from a woman, but another woman can. See more here.)
The text of havdalah is unchanged, except for the omission of the blessing over spices. The blessing over a flame is included only when havdalah is recited on Motzaei Shabbos (as opposed to Sunday) and if it had not been recited on its own previously (in Shul etc.).