The Way to Dua.
Almighty God is all-present and all-seeing, God responds to prayers of servants. Through His presence and response, He transforms the desolation of loneliness and solitude into familiarity. But He does this, not in accordance with man's capricious and importunate demands, but in accordance with the requirements of dominical wisdom; He gives either what is sought or what is better than it, or He gives nothing at all
"Call on Me; I will answer your (Prayer)" also means this: Call me so that I will answer you. That is, beg from me, I will provide you; you will find me. He who finds me finds everything because the following is stated in the Quran: "Verily, when He intends a thing, His command is "Be" and it is!" (Yasin, 36/82), which is the prayer that is never rejected. In some resources, the following is stated: "He who demands me finds me." Those who keep away from worshipping me, that is, who are too conceited to demand me through prayer will be kept away from me and will be despicable and humiliated in the hell of deprivation.
Allah Accepts and Answers Dua
Allah said, "there is no difficulty to you "as it is expressed by this verse: "There can be no difficulty to the Prophet in what Allah has indicated to him as a duty" (al-Ahzab, 33/38); He said the following to this ummah: "Allah doth not wish to place you in a difficulty" (al-Maida, 5/6) Allah said, "Pray to me; I will answer you." He said to this ummah: "Call on Me; I will answer your (Prayer)" (Ghafir, 40/60)
And your Lord says: Call upon Me, I will answer you."
[2.Surah Al-Baqarah : Ayah 186]
"And when My servants ask you concerning Me, then surely I am very near; I answer the prayer of the suppliant when he calls on Me, so they should answer My call and believe in Me that they may walk in the right way." [27.Surah Naml : Ayah 62
"Or, Who answers the distressed one when he calls upon Him and removes the evil, and He will make you successors in the earth. Is there a god with Allah? Little is it that you mind!"
Duas of Some Prophets
Dua of Hazrat Ayub (Alaihi Salaam)
"And Ayub, when he cried to his Lord, (saying): Harm has afflicted me, and Thou art the most Merciful of the merciful."
"Therefore We responded to him and took off what harm he had, and We gave him his family and the like of them with them: a mercy from Us and a reminder to the worshippers." Ayahs 87-88: Dua of Hazrat Zakariya (Alaihi Salaam)
Dua of Hazrat Yunus (Alaihi Salaam)
"And Yunus, when he went away in anger, so he thought that We would not straiten him, so he called out among afflictions: There is no god but Thou, glory be to Thee; surely I am of those who make themselves to suffer loss."
"So We responded to him and delivered him from the grief and thus do We deliver the believers."
Dua of Hazrat Zakariya (Alaihi Salaam)
"And Zakariya, when he cried to his Lord: O my Lord leave me not alone; and Thou art the best of inheritors."
"So We responded to him and gave him Yahya and made his wife fit for him; surely they used to hasten, one with another In deeds of goodness and to call upon Us, hoping and fearing and they were humble before Us."