1)  The Shulchan Aruch (561)  rules that when a person sees the Old City of Yerushalayim he should say, ציון היתה מדבר שממה , and then tear kriah. The Shulchan Aruch continues that a person who sees the site of the Beis Hamikdash should say בֵּית קָדְשֵׁנוּ וְתִפְאַרְתֵּנוּ אֲשֶׁר הִלְלוּךָ בּוֹ אֲבוֹתֵינוּ הָיָה לִשְׂרֵפַת אֵשׁ וְכָל מַחְמַדֵנוּ הָיָה לְחָרְבָּה and then rip kriah again. Upon ripping kriyah one also recites “Baruch Dayan Haemes” without reciting the name of Hashem.
2) A person can tear kriah when he sees the Dome of the Rock, which is located on the site of the Beis Hamikdash, or upon seeing the Western wall, whichever is seen first. (Shulchan Halevi page 152)
If one sees the Old City first, one has to rip, and then make a separate tear (3 fingerbreadths away) upon seeing the Kotel. He need not use a separate garment. Rather, he may rip the same garment in two locations. (Shulchan Halevi ibid.)
3) Rav Moshe Feinstein zt”l was of the opinion that one need not rip kriyah when seeing the Old city today since it is under Jewish leadership. He explains that it only is considered “in ruins” when it is under non-Jewish control. (Igros Moshe 4:70) However, Harav Yisroel Belsky zt”l disagrees with this view. He explains that since there are still churches and houses of worship in the Old City it is still considered in ruins and would warrant ripping kriyah. Asimilar view is cited in the name of Rav Shlomo Zalman Auerbach zt”l.(Minchas Shlomo 73) All agree that one rips kriyah upon seeing the kotel even today.
4) After ripping the garment one may remove the ripped garment and replace it with a whole garment, even though he is still standing near the kosel. (Netai Gavriel Bein Hamitzarim vol. 2 ch. 100)
5) One only rips a garment if he has not seen the kotel in 30 days.
6)The kriah can be started with a knife or razor, but a person must tear one tefach (approximately four inches) by hand. The kriah should be performed on the left side of the garment. (Shulchan Halevi ibid.)
7) The opinion of Harav Moshe Heinemann shlit”a is that a person who is performing kriah on a shirt should begin tearing kriah above the top buttonhole (or top button on a woman’s shirt), where the collar meets the shirt. (Kashrus Kurrents Winter 2013)
8) One rips standing up. (Shulchan Aruch 561:4) Therefore, if one is on the bus or taxi and he sees the Temple mount or the Old City, he should stand up before performing the kriyah. (Netai Gavriel ibid. Page 585)
9) A child under the age of Bar or Bat Mitzvah need not rip kriyah. (Netai Gavriel ibid.)
10) Women must also rip kriyah. They must ensure, however, to have a jacket or coat to cover over the rip so as to avoid issues of tznius. Or she should pin the tear back after tearing. (See Netai Gavriel ibid.)
The chosson and kallah are exempt from tearing their clothing during the seven festive days. (Hanisuin K’Hilchosom page 574)
11) There is a custom not to rip kriyah on Erev Shabbos after midday (and on Chol Hamoed). Although there is no real source for this custom, nevertheless this is the common custom. The poskim discuss whether one should rip kriyah the second time he sees the kotel when it is not Erev Shabbos. Harav Shlomo Zalman Aeurbach zt”l discusses a similar situation. He writes that if one sees the kotel for the first time on Shabbos, he does not rip kriyah on Motzei Shabbos. He explains that ripping kriyah only applies to the first time one sees the kotel. If, however, the first time was Shabbos he no longer rips the second time. (Unless 30 days have passed between the two visits) Halichos Shlomo vol. 1 ch. 16 note 7. Harav Moshe Shternbuch shlit”a (Teshuvos V’Hanhagos 1:354) applies this view to Erev Shabbos as well. Meaning if one saw the kotel for the first time on Erev Shabbos after midday, he does not rip kriyah even during the second time he sees the Kotel. This is also the view of the Netai Gavriel. However, Harav Yisroel Belsky zt”l disagrees and maintains that if one sees the kotel for the first time on Erev Shabbos, then on the second time after Shabbos he needs to rip kriyah.
12) Many have the custom to be makneh (transfer the ownership) their garment to someone else to exempt themselves from ripping. The kinyan works in the following manner: someone hands you his pen (or similar item) in order to acquire your shirt; you then return the pen. Since the shirt no longer belongs to you, you do not have to rip, even though you are wearing it. However, Harav Belsky zt”l was not in favor of this custom and he maintained that one should rip kriyah and show genuine grief over the loss of our Beis Hamikdash.