A few points I learned on Dua's (Supplication)

In a Hadith-e-Qudsi*, Prophet Mohammed (SwalAllahu Alaihi Wasallam) has said that he heard Allah Ta'ala saying, "I will be for my slave as he sees me". So, see Allah Ta'ala as your sustainer, your nurturer, your cherisher, your provider, your saviour and that is what He will be for you.

Dua (Supplication) is the only thing that can change what is written (taqdeer). Nabi Ibrahim (AS) made dua for a son for 70 years (according to some narrations). This is a clear lesson that in a mo'min's (believer) life, patience is key and dua is constant. Allah Ta'la may not grant you exactly what you ask for, but he WILL grant you what is best for you and that too at a time that is most appropriate for you.

It is important to understand and remember that making dua cannot be a selfish act for a Muslim. A Muslim makes dua for themselves, family, friends, neighbours, the community, the Ummah and humanity. It is said that when you make dua for someone else, Allah Ta'ala appoints Malaaika (angels) to make the same dua for you.

Nabi (SAW)'s Dua 

Oh Allah, grant me light in my flesh, 

grant me light in my eyes, 

grant me light in tongue, 

grant me light in my ears, 

grant me light in my hands, 

grant me light in my feet, 

let there be light inside of me,

let there be light outside of me, 

let there be light above  me, 

let there be light below me, 

let there be light in front of me, 

let there be light behind me, 

let there be light on the right of me, 

let there be light on the left of me, 

let there be light all around me. 

Oh Allah, make me your light.

Hazrat Umar (RA)'s Dua

Oh Allah, grant me Shahaada in your path and make my death in the land your Beloved Rasool (SAW).

Some  other Dua's

• Oh Allah, look after me like a small child
• Oh Allah, look after our parents like they looked after us when we were children
• Oh Allah, make the Muslim Ummah an illuminated and elevated Ummah, let us be identified by the light that illuminates from us, let this light be a source of unity for us.
• Oh Allah, shower me with your love and with the love of those who love thee
• Oh Allah, let me be your agent in spreading the light of deen (religion)
• Oh Allah, give me the opportunity to see people entering this perfect deen
• Oh Allah, don't let our beloved Nabi (SAW) be embarassed by us on the day of judgment. Hide our sins from him on this day.
• Oh Allah, let our parents be content with us and let us be their pillar of strength
• Oh Allah, link our heart with the heart of our Beloved Nabi (SAW)
• Oh Allah, let our heart be the container of the Glorious Qur'aan and let our tongues speak its language and let our minds comprehend its message and let us be the embodiment of it
• Oh Allah, look after the orphans of this world and the oppressed of this world
• Oh Allah, let us be in the company of the pious and let us learn from them
• Oh Allah, make us from those whom you have befriended 
• Oh Allah, make us from those who make the best Tauba and perform the best deeds.
• Oh Allah, you are peace and from you comes peace, so give me peace

May Allah grant us all our duas.
Ameen

* Hadith-e-Qudsi is a Hadith where Nabi (SAW) heard Allah Ta'ala saying something.