In the Name of Allah, Most Gracious, Most Merciful. All praise and thanks are due to Allah, and peace and blessings be upon His Messenger
For Muslims there are three types of prostrations which should be performed accordingly as follows:
Prostration of Forgetfulness(sujjud us-sahu)
The “prostrations of forgetfulness” (sujjud us-sahu) are two prostrations which a person makes before the taslim.. If one of you has some doubts during his salah and he does not recall (the number of rak’at) he has prayed, three or four, then he can put an end to his doubt by performing salah according to what he was certain of [the lesser amount] and then making two sujjud before the taslim. If one forgot any rak’at and did his taslim then he should make that missing rak’at and then perform two sujjud after taslim. Same thing goes for praying any additional rak’at like five instead of four or four instead of three.
In the case of forgetting the first tashahud or one of the other sunnah acts of the prayer. This hadith shows that one who forgets the first sitting but is reminded of it and he recalls it before he completely stands should return and sit, but if he is already completely standing, he should not sit and he should make two sujjud of forgetfulness after taslim
Prostration of Recital (Sujjud us-Tilawah)
Whoever recites an “‘ayyah of prostration (sajdah)” or hears an “‘ayyah of prostration” should preferably pronounce the takbir and prostrate and then make the takbir again and rise from the prostration. This is called “the prostration of recital.” There is no tashahud or taslim with the sajdah. This sujjud is Sunnah, whoever does so has acted correctly, while, there is no sin upon one who does not do so.
The majority of the scholars lay down the same conditions and prerequisites for the prostration of recital as they do for the salah, with respect to purity, facing the qiblah, and covering the ‘aurah. One may make any du’a during this sujud and should say three times Subhana Rabbi-yal aa-la . This sajdah is to be performed right after the recital or hearing of the ‘ayyah.
Prostration of Thankfulness (Sajdat ush-Shukr).
The majority of the scholars say that it is preferred to make prostrations of thankfulness (shukr) when one receives a bounty or is rescued from some trial. There is nothing in the hadith to prove that ablution and purity of the clothes and place are required for sajdat-ush-shukr. And that is the opinion of Imam Yahya and Abu Talib. And these hadith are silent about any takbir being made with the prostration. In alBahr it is stated that there is a takbir.
Source: Fiqh us-Sunnah Vol. 2 by As-Sayyid Sabiq