Why and how to call upon Allah in my prayer?.
Allah Almighty says in Aya (60) of Surat Ghafir {And Your Lord said, Call upon Me, I will respond to you, indeed, those who are arrogant to worship Me will enter Hellfire, humiliated}. Thereupon, Allah promises His servants that He will respond to their supplication, but Allah has set conditions for the supplication to be answered, including that the servant responds to Allah and submits to Him with obedience and submission, as Allah addresses His Messenger Muhammad (PBUH) in Aya (186) of Surat Albaqarah saying {And when My servants ask You concerning Me, indeed, I am near, I respond to the supplication of the supplicant when he calls upon Me, so Let them respond to Me, and believe in Me, so that they may be rightly guided}, or that He does not supplicate for sin or severing of ties of kinship, or that he does not hasten the answer and does not abandon the supplication, as Abu Hurayrah narrated that the Messenger of Allah (PBUH) said: "The supplication of the servant is granted in case he does not supplicate for sin or for severing the ties of womb, or he does not become impatient, it was said Messenger of Allah! What does "if he does not grow impatient'' imply?, He said that he should say I supplicated and I supplicated but I did not find it being responded, and then he becomes frustrated and abandons supplication" (Sahih Muslim 2735 c).
Supplication during prayer while prostrating is one of the greatest and best times for the supplication to be answered, as Abu Hurayrah narrated that Allah's Messenger (PBUH) said: "The closest a servant comes to his Lord is when he is prostrating, so Supplicate frequently" (Sahih Muslim 482), and in another narration of Ibn Abbas, the Messenger of Allah (PBUH) said: "Indeed, I have been forbidden to recite the Quran in the state of bowing and prostration, as for bowing (Ruku'), Extol in it the Lord, the Almighty and Majestic, and as for prostration, Be earnest in supplication, for it is worthy that your supplications will be answered" (Sahih Muslim 479).
And as narrated by Abu Hurayrah, Allah's Messenger (PBUH) used to say while prostrating Himself: "Allahumma ighfir lee zanbi kullahu, diqqahu wa jellahu, wa awwalahu wa akherahu, wa alaniyatahu wa serrahu: O Allah! Forgive Me all My sins, small and great, first and last, and open and secret" (Sahih Muslim 483). And as narrated by Hudhaifa: "The Prophet (PBUH) used to say between the two prostrations Rabbi ighfir lee, Rabbi ighfir lee: O Lord! Forgive me, O Lord forgive me" (Sunan Ibn Majah 897).
In addition to the position of prostration, the Prophet (PBUH) would supplicate upon Allah in more than one position during His prayer. He (PBUH) would begin the prayer after the first Takbir (Allahu Akbar: Allah is the Greatest) and before reciting Surat Alfatihah with the opining supplication, as Abu Hurayrah reported: "Allah's Messenger (PBUH) used to keep silent between the Takbir and the recitation of Quran, and that interval of silence used to be a short one, I said O Messenger of Allah! My father and my mother be sacrifice for You, What do You say in the pause between Takbir and recitation?, He (PBUH) said I say Allahumma baa'id baiyni wa baiyna khatayaya kama baa'adta baiyna almashriqi wa almaghrib, Allahumma naqqini men khatayaya kama younaqqa althawbu al-abyadu mena aldanas, Allahumma ighsil khatayaya bel-maa'i wa althalji wa albarad: O Allah! Set Me apart from My sins as You have set apart the East from West, O Allah! Cleanse Me from sins as a white garment is cleaned of dirt, O Allah! Wash off My sins with water, snow, and hail" (Sahih Albukhari 774).
And Allah's Messenger (PBUH) would supplicate Allah between the final Tashahhud and Taslim (Salutation), as Abu Hurayrah narrated that the Messenger of Allah (PBUH) said: "When anyone of you utters Tashahhud, he must seek refuge in Allah from four and should say Allahumma inni a'auzu beka men azabi jahannama, wa men azabi alqabri, wa men fetnati almahya wa almamati, wa men sharri fetnati almasihi aldajjal: O Allah! I seek refuge in You from the torment of Hellfire, from the torment of the grave, from the trial of life and death, and from the evil of the trial of the false Messiah (Antichrist)" (Sahih Muslim 588).
And Ali bin Abi Talib reported that among the last thing the Messenger of Allah would say between Tashahhud and the pronouncing of Salutation (Taslim) when he got up at night for prayer is: "Allahumma ighfir lee ma qaddamtu wa ma akhkhartu wa ma asrartu wa ma a'lantu wa ma asraftu wa ma Anta a'lamu behi minni, Anta Almuqaddimu wa Anta Almu'akhkhiru la ilaha ella Anta: O Allah! Forgive Me for what I have done before and later, what I have concealed and what I have made public, and what I have done excessively, and what You know better than I do. You are the One who makes people forward, and You are the One who makes people backward, there is no god but You" (Sahih Muslim 771).