Sajdah tilawat is the sajdah that one has to perform as an obligatory duty when one reads, recites, or hears, in the prayer or outside, some specific verses containing those words. The Holy Prophet, Sall-Allahu alayhi wa sallam, has observed, "One a person prostrates himself after reading a verse requiring the performance of sajdah, the shaitan starts crying and wailing in a corner, saying: 'Alas! The children of Adam were enjoined to perform sajdah and they carried it out, and become entitled to enter Paradise, but I refused to do so and was condemned to Hell.'" (Muslim and Ibn Majah)
There are four pre-requirements:
Purity of body, clothes, and place of sajdah.
Covering of satr.
Turning your face toward qiblah.
Intention of performing sajdah.
Stand facing the qiblah.
Express the necessary intention.
Go down for sajdah with Allahu-Akbar.
Rise up with Allahu-Akbar after sajdah.
"When you have recited a verse requiring sajdah tilawat, you should go down for sajdah with Allahu-Akbar and rise from sajdah with Allahu-Akbar, which may be performed sitting, though it is preferable to prostrate oneself from the standing position." (Abu Dawood)
It is obligatory for those persons only who have to perform and observe the prayers (for example it is not obligatory for a child).
If a verse requiring a sajdah has been recited inside the prayer, the sajdah has to be performed forthwith, but if the verse is recited outside the prayer, it is preferable to perform sajdah soon afterwards, but one may perform it later as well.
If a verse requiring the performance of sajdah has been recited in a particular prayer, it is obligatory to perform the sajdah in the same prayer, neither outside it nor in another prayer. If a sajdah is omitted in forgetfulness, one should ask Allah for forgiveness.
If a person hears a verse requiring a sajdah, being recited by the Imam, but joins the congregation when the Imam has already performed it, he will perform the sajdah after completing his prayer. There will be no need for performing the sajdah later if the follower has joined the congregation in the rak'ah in which the sajdah is performed by the Imam.
If a person recites a verse requiring a sajdah in the mind but does not utter it aloud or only writes it, he will not be required to perform the sajdah.
If the verse requiring a sajdah is recited over and over again in the same sitting, only one sajdah will have to be performed, but if more than one verse requiring sajdahs are recited, the number of sajdahs to be performed will be the same as the number of the verses recited. Similarly, if the verse requiring a sajdah is repeated in different sittings, the number of sajdahs to be performed will be according to the number of sittings.
Some ignorant people prostrate themselves on the Qur'an itself when they have recited a verse requiring a sajdah. This is not valid.