Tisha Be-Av which Falls on Motzaei Shabbat

1. Beginning of the Fast
The fast as well as the other prohibitions begin from sundown – not nightfall (i.e. when 3 stars come out), even though it is still Shabbat (Mishnah Berurah 552:24).

2. Seudah Mafseket
It is permissible to eat meat and drink wine and have a festive meal like King Shlomo (Shulchan Aruch, Orach Chaim 552:10).  And one does not eat an egg dripped in ashes as in a regular year.  There are Poskim who say that one should nonetheless eat the meal in a sorrowful manner without joy, and without company, while other authorities permit acting as on all other Shabbatot, so there is no public mourning on Shabbat (Mishnah Berurah #24).  One must be careful, however, to complete the meal before sunset (Mishnah Berurah ibid.).

3. Removing Shoes
The Rama (Orach Chaim 553:2) rules that on Tisha Be-Av which falls on Motzaei Shabbat, we remove our shoes after Barechu of Maariv, since it is forbidden to display any signs of mourning on Shabbat (Mishnah Berurah #6).  The Rama adds, however, that the Shaliach Tzibur removes his shoes before Barechu, after reciting "Baruch Ha-Mavdil Bein Kodesh Le-Chol" (Mishnah Berurah Ibid. #7).  The Mishnah Berurah (Ibid.) explains that he does so in order not to become confused if he has to remove them after Barechu.
There are however various problems which arise with this:
a. One who brings his Tisha Be-Av shoes to Shul on Shabbat violates preparing on Shabbat for a weekday.
b. When one removes his shoes and puts on his Tisha Be-Av shoes, he must be careful not to touch them, or he will be required to wash Netilat Yadayim.
c. Everyone changing shoes impinges upon proper intention while Davening.
d. If everyone changes their shoes (even if they brought them to Shul before Shabbat), the Shul will be filled with shoes, which disgraces the holiness of the Shul.
It is therefore preferable to act in the following manner: After nightfall (3 stars coming out), before one leaves his house, each person says "Baruch Ha-Mavdil Bein Kodesh Le-Chol" and puts on his Tisha Be-Av shoes (and see Shut Yechaveh Daat 5:38).  In order to do so, Maariv should be delayed 15 minutes.  If one is unable to act in this manner, he should put on his Tisha Be-Av shoes at home on Shabbat and walk to Shul in them so he is not preparing on Shabbat for a weekday, since he is using them on Shabbat itself.  Even though this seems to contradict the concept of not displaying signs of mourning on Shabbat, our Sages allow one to wear regular shoes on Tisha Be-Av if one is traveling or if one lives among non-Jews and he fears being mocked (Shulchan Aruch, Orach Chaim 554:17), and the same leniency applies for the honor of Shabbat and he may wear his Tisha Be-Av shoes on Shabbat.

4. Kinot
One who brings a Kinot book to Shul on Shabbat should learn a little from it so that he does not prepare on Shabbat for a weekday.

5. Havdalah
After Maariv, before reciting Kinot, we recite only the blessing over seeing a candle (and not the verses before Havdalah or the Berachot over wine and spices).  If one does not recite the blessing then, he should do so later that night upon seeing a candle or light.  A woman should also recite this blessing if she stays at home and her husband does not return until later.  On Motzaei Tisha Be-Av (Sunday night), we recite Havdalah only over wine, without a candle and spices (Shulchan Aruch, Orach Chaim #556).  We also do not recite the verses before Havdalah.     

6. Eating   
When Tisha Be-Av is postponed until Sunday – those who are ill, nursing or pregnant fast as long as it is not difficult for them.  If it is difficult for them, it is permissible for them to eat.  There is no need to eat "Shiurim" (minimum quantities), but one should eat simple foods.
Anyone who eats should first recite Havdalah over grape juice.

7. Motzaei Tisha Be-Av when Tisha Be-Av is Postponed
After the fast, it is forbidden to eat meat and drink wine.  It is permissible to drink wine during Havdalah.  It is permissible to do laundry and get a haircut and shave.  All of the other Halachot of the Three Weeks no longer apply (Halichot Shlomo of Ha-Rav Shlomo Zalman Auerbach Chapter 15, Dvar Halachah #26.  Unlike the ruling of Ha-Rav Yechiel Michal Tukachinsky in Luach Eretz Yisrael).  In the morning, all of the prohibitions of the Three Weeks are lifted.

May Hashem continue the return of His Presence to Zion, and may the Beit Ha-Mikdash be built speedily in our days.