All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There are many ways to have one’s supplications (Du’aa') responded to by Allah. Some of them are as follows:
1. The supplication is responded to when it is from a Muslim for his fellow brother in his absence, as the Prophet said: “If a Muslim supplicates Allah for his Muslim brother (without the knowledge of this brother), Allah answers his supplications. An angel says to him ‘Amen’ and says: ‘May it be for you as well.’" [Abu Daawood and Ibn Maajah]
2. Making Du’aa' during special times, such as in the night of Al-Qadar (the night of Decree which is better than 1,000 months), in the last part of every night, during the Friday Khutbah, between the time of the Athaan and the Iqaamah, at the time when rain falls, when Muslims and non-Muslims meet in a battle during war, supplication said near the Ka’bah, during a journey, and while fasting. Sometimes Allah favors some pious people by responding to their supplications as He accepted the Du’aa' of Sa’d ibn Abu Waqqas .
The person who wishes to have his supplication accepted should consume only lawful earnings since the Du’aa' of a person who consumes ill-gotten earnings is seldom accepted by Allah.
For more benefit on supplications, please refer to Fataawa 343300, 88282, 13277, 213715 and 377509.
Allah knows best.