Salat al-Hajah is a prayer offered for the accomplishment of a particular purpose or need. It consists of a fresh ablution done carefully, followed by a calm prayer of two rak'ahs, then a sincere supplication that states what one wishes to be accomplished and requesting Allah Ta'ala's help in its accomplishment.
Abu Darda (RA) relates that the Messenger of Allah (salAllahu alayhi wasalam) said, "Whoever performs ablutions well and offers two voluntary rakahs and completes them to perfection will be granted by God whatever he prays for, either immediately or in God’s good time."
[Ahmad - Sahih]
La ilaha ilAllahul Halimul Karim. SubhanAllahi Rabbil 'rshil adheem. Alhamdulilahi Rabbil 'alameen. As'aluka mujibaati rahmatik. Wa aza'ima magh-firatik. Wal ghanimata min kulli birr. Was salamata min kuuli ithm. La tada' li dhamban illa ghafartah. Wa la hamman illa far-rajtah. Wa la hajatan hiya laka ridan illa qadaytaha. Ya arhamar rahimin.
"There is no god but Allah the Clement and Wise. There is no god but Allah the High and Mighty. Glory be to Allah, Lord of the Tremendous Throne. All praise is to Allah, Lord of the worlds. I ask you (O Allah) everything that leads to your mercy, and your tremendous forgiveness, enrichment in all good, and freedom from all sin. Do not leave a sin of mine (O Allah), except that you forgive it, nor any concern except that you create for it an opening, nor any need in which there is your good pleasure except that you fulfill it, O Most Merciful!"
The inward manners of supplication is exhibiting our neediness and absolute slavehood to Allah, consigning one's matters to Allah, and knowing that the only one who gives or benefits is Allah Most High. With this, one should be certain that Allah Most High answers our duas, but in the way He knows is best for us.
Source: Mutmainaa & Sunnipath