Read this dua when you open your fast.

“O Allah, I ask You by Your mercy, which encompasses all things, that You forgive me

اللّهُـمَّ إِنَّـي أَسْـأَلُـكَ بِرَحْمَـتِكَ الّتي وَسِـعَت كُلَّ شيء، أَنْ تَغْـفِرَ لِي

Allaahumma ‘innee ‘as’aluka birahmatikal-latee wasi’at kulla shay’in ‘an taghfira lee.

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Ibn Majah 1/557 from a supplication of Abdullah bin ‘Amr. Al-Hafidh graded it as good in his checking of An-Nawawi’s Kitabul-‘Athkar.

Method of Supplicating

One should supplicate after doing Wudhu.
Supplicate facing the Qibla.
One should supplicate with both hands raised.
Before Dua, one must recite the praise and glorification of Almighty Allah.
Recite Durood-e-pak before and after reciting supplication. (It is given at the end of this section).
Never supplicate for an unlawful thing or cutting off of relations.
Supplicate with presence of mind.
One must have a good notion about Almighty Allah that He is kind, and He would not return the supplicant empty handed.
One should be absolutely attentive to Almighty Allah.
One should supplicate fervently.  One should mention the needs.  One must include others also in one’s supplications.
One must express his humility and weakness before Almighty Allah.
Give Sadaqah (charity) before supplicating, if possible
Supplicate before the arrival of calamity. Holy Prophet (Peace be upon him) says: You should recognize Almighty Allah during prosperity and He will come to your help when you are in trouble.
You should request brothers in faith to pray for you as the Almighty accepts the supplication of one believer for another.
Continue to supplicate regularly whether your supplication is answered or not; perhaps there is some divine exigency in the delay and dua is loved by Almighty Allah, thus one should never give up the most liked act.

Say “Ameen” at the end of making dua.

After the supplication, pass both hands over the face.

Along with supplication, one must abandon all the unlawful acts and disobedience of Allah as bad intentions, internal evil, hypocrisy, delay in ritual prayer and disobedience of parents hinder acceptance of supplications.

The best times for making dua

The last third of the night
Late at night
While prostrating
Between Adhan and Iqamah
While drinking Zamzam Water
When Waking Up at Night
At The End Of The Obligatory Salat
At the time of Tahajjud
The Night Of ‘Qadr’ (Decree)
During the rain
During a special hour on Friday (between Asr and Maghrib)
While travelling
During the month of Ramadhan
Shab e Qadr
Day of Arafah
During sickness etc

Durood e paak

Read durood e paak before and after making dua.

Durood means to send peace and blessings on our HOLY PROPHET (PEACE BE UPON HIM). It is a great act of worship.
”Indeed,Allah and His angels send blessings on the Prophet: O you who have believed, Send ye blessings on him, and salute him with all respect” [33:56]
”O Allah, bestow Your favor on Muhammad (Peace be upon him) and on the family of Muhammad (Peace be upon him) as You have bestowed Your favor on Ibrahim (Peace be upon him) and on the family of Ibrahim (Peace be upon him), You are Praiseworthy, Most Glorious.
O Allah, bless Muhammad (Peace be upon him) and the family of Muhammad (Peace be upon him) as You have blessed Ibrahim (Peace be upon him) and the family of Ibrahim(Peace be upon him) , You are Praiseworthy, Most Glorious”
اللَّهُمَّ صَلِّ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ، كَمَا صَلَّيْتَ عَلَى إِبْرَاهِيمَ، وَعَلَى آلِ إِبْرَاهِيمَ، إِنَّكَ حَمِيدٌ مَجِيدٌ، اللَّهُمَّ بَارِكَ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ كَمَا بَارَكْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ، إِنَّكَ حَمِيدٌ مَجِيدٌ
Allahumma salli alaa muhammadin wa alaa aali muhammadin kamaa sallaita alaa ibrahima wa alaa aali ibrahima innaka hameedum majeed
Allaahumma baarik alaa muhammadin wa alaa aali muhammadin kamaa baarakta alaa ibrahima wa alaa aali ibrahima innaka hameedum majeed

http://dua.2learnislam.com/category/duas-from-the-hadith/miscellaneous-duaas/durood-e-paak/