The verse of “Adono-y Sefasaiy Tiftach” recited before Shemoneh Esrei:
It is an obligation to recite the verse of Adono-y Sifasaiy Tiftach prior to starting Shemoneh Esrei, due to a Rabbinical institution. Due to this institution, this verse is considered as an actual part of Shemoneh Esrei and like an extension of it. [Thus, one is to already take three steps forward and place the feet together, prior to saying it, and is not to take the steps back and forth while saying it.]
Reciting it after Goal Yisrael: Although it is forbidden to make an interval in the Shacharis prayer between Goal Yisrael and the start of Shemoneh Esrei, it is permitted to recite the verse of Adono-y Sifasaiy Tiftach prior to starting Shemoneh Esrei.
Making an interval after reciting the verse: It is forbidden to make an interval [for any purpose, including Kaddish, Kedusha] once the verse of Adono-y Sifasaiy Tiftach has been recited prior to Shemoneh Esrei, just as it is forbidden to make an interval in middle of Shemoneh Esrei. This applies by all prayers, including Musaf and Mincha [and certainly to Shacharis and Maariv].
Chazan repeating: When the Chazan repeats Shemoneh Esrei aloud, he must first say the verse of Adono-y Sifasaiy Tiftach. This verse is said quietly by the Chazan [and only then does he begin the repetition aloud].
The meaning of the verse and why it is said before Shemoneh Esrei:
The verse of Adono-y Sifasaiy Tiftach was said by David Hamelech as a supplication to Hashem that his prayers be accepted despite his sin with Batsheva. The reason for this is as follows: The next verse in Tehillim speaks of that Hashem does not accept sacrifices for sins that were done advertently. Hence, David Hamelech, who had advertently sinned with Batsheva, made a special request from Hashem that his prayers be accepted in place of a Karban, and that he be successful in praising G-d and concentrating in his prayers. It is for a similar reason that we say this verse today prior to Shemoneh Esrei, as since due to the lack of the Temple we cannot bring Karbanos, we ask Hashem that our prayers be accepted in place of the Karban. Thus, this verse teaches us that even those who have committed sever sins advertently, can achieve atonement through prayer. [This verse expresses nullification and subservience towards Hashem and helps the prayer be accepted.]
The Kabalistic meaning:
Shemoneh Esrei corresponds to the spiritual world of Atzilus. The verse of Adono-y Sifasaiy Tiftach corresponds to the highest level of Beriyah, known as the Kodesh Kedoshim of Beriya. This verse serves as a stepping stool to reach the world of Atzilus in Shemoneh Esrei.
 Admur 111:1; Michaber 111:1; Tur 111; Rebbe Yochanon in Brachos 4b; 9b
 Tehillim 51:17
 Admur ibid; Taz 111:2
 Beir Moshe 5:50; Piskeiy Teshuvos 111:2
 Admur ibid; Michaber ibid; Tur ibid; Rebbe Yochanon Brachos 4b
 The reason: As it is not considered an interval. The reason for this is because the Sages instituted for it to be said as part of Shemoneh Esrei, and it is thus considered as actual part of Shemoneh Esrei and like an extension of it. [Admur ibid; Taz 111:2; Brachos ibid]
Other reason: Some Poskim write that this verse is considered an extension of the blessing of Goal Yisrael, and not as part of Shemoneh Esrei. [Tur 111 “Geula Arichta”, brought in P”M 111 M”Z 2; However, see Bach and Beis Yosef ibid who correct this wording that it should say “Tefila Arichta”]
 Admur ibid; M”A 111:1; Lechem Chamudos Brachos 53; M”B 66:35 in name of Elya Raba
 Implication of Admur and Poskim ibid; M”B 66:35 in name of Elya Raba
Other opinions: Some Poskim rule it is permitted to make an interval between this verse and Shemoneh Esrei in order to answer for Kaddish, Kedusha and Barchu. After answering one is to then repeat the verse. [Makor Chaim of Chavos Yair 122:1; Ben Ish Chaiy Vayakehl 10; Rav Poalim 4:4] See Chayeh Halevi 2:10; Piskeiy Teshuvos 111 footnote 14
 The reason: As this verse is considered part of the actual Shemoneh Esrei. [Admur ibid; Machatzis Hashekel ibid]
 Admur 111:3; Michaber 111:2; 123:6; Terumas Hadeshen 2:110
Other opinions: Some Poskim rule that the verse of Adono-y Sifasaiy Tiftach is considered an extension of the blessing of Goal Yisrael, and not as part of Shemoneh Esrei. [Tur 111 “Geula Arichta”] According to this opinion, there is no need for the Chazan to repeat it prior to his repetition. [P”M 111 M”Z 2]
 The reason: As this verse is considered part of the actual Shemoneh Esrei. [Admur ibid]
 Admur ibid; M”A 111:4; Kisvei Arizal [of other students of Arizal, not Rav Chaim Vital-Kaf Hachaim 111:10]
Other opinions-Sefaradim: Some rule that the Chazan to recite the verse of Adono-y Sifasaiy Tiftach aloud, just like the rest of his repetition. [Kaf Hachaim 111:10 that so is implied from Michaber ibid and so is the implication of Arizal in Shaar Hakavanos Chazaras Hamida Derush 1] Practically, so is the custom of the Sefaradim. [Kaf Hachaim 111:10 that so is custom in Beis Keil , and all other Jerusalem Shuls]
 Rabbeinu Yona Brachos 9b, brought in Beis Yosef 111; P”M 111 A”A 1
 P”M 111 A”A 1
 Arizal in Shaar Hakavanos Derushei Amida 1 [see there in great length]