There are five elements that cause the du3aa to be answered:

I. A Reason related to the one making du3aa, or a state in which he is in that makes his more likely to be answered (as mentioned in the Quran and Sunnah), examples include:
1) fasting person
2) traveller
3) one who is oppressed
4) a pious child who makes du3aa for his parents

II. A Reason related to the du3aa itself; meaning the ettiquettes of du3aa are adhered to so that the du3aa may be perfected:
 1) begin by praising Allah and sending prayers and blessings upon Rasoolullah (saws)
 2) gain nearness to Allah through tawassul, either by:
    a. calling upon Allah by His names and attributes
    b. calling upon Allah by one's good deeds
    (ex. like saying "O Allah, I have beautiful hair and I covered it for your sake and for no other reason")
 3) Be on wudu
 4) Face the Qiblah
 5) Never ask for that which is Haraam (such as breaking ties of kinship
 6) Ask about anything and everything you need and the best way is to generally asked for the good of dunya and aakhirah
 7) Make you du3aa contingent upon Allah's knowledge (for examples say: Allah give me such-and-such "if it is good for me" because only He truly knows what is good for you.)
 8)Insist for it, beg, stay determined to get it b/c you are fully dependent on Him.
 9) Don't use "if you want/will to" because Allah does what he wants.
10) Raise hands to shoulder level with palms facing towards the sky
11) Lower one's gaze in humility and don't look to the sky
12) Lower one's voice in humility, don't say it aloud
13) End your du3aa with praise of Allah and prayers upon Rasoolullah
13) Be patient in waiting for the response:
Rasoolullah (saws) teaches us that whenever anyone makes du3aa, he will be answered unless he says "Allah didn't answer me." And if he is not answered in this dunya then either Allah will remove from him some harm in
this dunya because of his du3aa or he will save his reward for him on the Day of Judgement.

III. Special Times when duaa'is most likely to be answered:
 1) when it's raining (rain is blessing from ALLAH)
 2) Last 3rd of night esp. before Fajr; called Sahr
 3) Between Adhan and Iqama
 4) Standing at mount 'Arafat (part of Hajj)*
 5) During the Qoonoot of Taraweeh in Ramadan
 6) Lailatul Qadr
 7) Friday, after Asr till Maghrib
 8) When a fasting person breaks his fast
 9) Before drinking Zam-Zam
10) Right after salah**
11) In sujood
12) etc...

IV. That there be no obstacles for the du3aa to be answered: This usually refers to one's relationship with Allah. Does one truly feel dependant and humble in front of Allah? Does one truly believe that Allah has the power to do whatever He wishes? And most importantly, is this person so sinful, having no regard for Allah's commands, yet he expects Allah to grant him what he wishes for? If one's food, drink, and clothing are all from Halal sources, Allah would not honor such a person with a response as is mentioned in a hadith.

NOTE: However, all humans are sinners, and they may , at any time, choose to change and come back to Allah. True tawbah means that one's istigfar changed their heart and being. This is what all of us should seek. Allah accepts the repentance from his servants if they are sincere. Even if we have sinned so much, we must always call upon Allah, for we cannot live without His blessings and sustenance. In fact, to not make du3aa is another sin which angers Allah. So if one fears that his du3aa may not be answered because of sins, let him begin his du3aa with istighfar and its conditions of acceptance are the following:
 1) immediately stop the sin and anything related to it.
 2) regret what you did sincerely.
 3) to promise never to return to that sin
 If it is between you and another person, then also:
 4) ask their forgiveness

*fasting on the day of 'Arafah (for non-pilgrims) is highly recommendedand and will expiate a preceding and future year of sins.

**Du3aa may be said in any language however in salah, only Arabic is allowed. Also it is not from the sunnah to immediately start du3aa after tasleem. Rather one should first say the following words from the sunnah: Astaghfirullah 3 times then Allahuma antas salaam wa minkas salaam tabrakata wa ta3alayta ya dhal-jalalee wal-ikram...

NOTE: For those who seek to gain tawassul to Allah, it is extremely helpful to memorize the 99 names of Allah and use them in your duaa'