بـسـم الله والحـمـد لله والـصلاة والـسـلام عــلى رسـول الله، وبـعـد
Shaikh Ibn Baaz رحمه الله , in his explanation to "Riyaadh al-Saaliheen", said: “The Sunnah before (beginning) the du`aa is to praise Allaah as has been mentioned in ‘al-Tahiyyaat’*, then after that to send the prayer upon the Prophet صلى الله عليه وسلم, then (he should make) the du`aa. And this is how it should be done also when he is making the du`aa in Sujood (prostration), or at any other time; he should praise Allaah, send prayers upon the Prophet صلى الله عليه وسلم and then supplicates to his Lord for whatever he wishes, and this is the first step for the du`aa being answered.”
Narrated Fudalah ibn Ubayd: The Messenger of Allaah صلى الله عليه وسلم heard a person supplicating during prayer. He did not mention the greatness of Allaah, nor did he invoke blessings on the Prophet صلى الله عليه وسلم. The Messenger of Allaah صلى الله عليه وسلم said: “He made haste.” He then called him and said either to him or to any other person: "When anyone of you makes du'aa, let him start by glorifying his Lord and praising Him, then let him send blessings upon the Prophet صلى الله عليه وسلم, then let him pray for whatever he wants" [Abu Dawud 1481 & Tirmidhi 3477, authenticated by Shaikh al-Albaanee in Saheeh al-Jami` # 648]
*"Al-Tahiyyaat" is what is also known as "al-Tashahhud", and the praise of Allaah is that which is mentioned at the beginning of it:
التَّحِيّـاتُ للهِ وَالصَّلَـواتُ والطَّيِّـبات
(At-tahiyyaatu lillaahi, was-salawaatu wat-tayyibaatu)
"At-tahiyyat is for Allaah. All acts of worship and all goodness are for Him"
The Shaikh رحمه الله gave an example here, a person can also use other words of praises mentioned in the Book and the Sunnah.