In Sajda, it is necessary that the face (the forehead and the nose), both the palms, both knees and both feet touch the ground. Out of these, the forehead and at least 1 finger of any foot is Fardh (obligatory).
The meaning of the word Sajda is to bow with humility and to touch forehead on the ground. The Sajda is to respect and bow to the greatness of the Lord Almighty Allah (Subhanahu Wa Ta'ala) and lifting both legs off the ground is more akin to some kind of play than respect, which is against the spirit of respect. As given in Radd Ul Muhtaar, Vol. 1, Pg. No: 330.
Imam Rafa'i (May Allah Ta’ala shower His mercy on him) has written in At Tahreer Al Mukhtaar Li Radd Ul Muhtaar:
Touching 1 finger of any foot is enough to complete the Fardh (obligation), as if in Sajda, if both the feet are lifted off the ground and not even 1 finger of any foot is not on the ground then the Sajda will not be correct as per the Shariah and the Salaat will be rendered invalid (Batil in Urdu). As given in At Tahreer Al Mukhtaar Li Radd Ul Muhtaar, Vol. 1, Pg. No: 56.
If the place where the Sajda is being offered such that the forehead touches the ground and the head does not go down too much then the Sajda is correct and with it the Salaat is also valid. On the other hand, if the place where the Sajda is being offered so soft that the forehead does not touch the ground and the head keeps bobbing, then the Sajda (and consequently the Salaat) is also not correct. However, if one feels the hardness of the surface while prostrating and the head touches the ground and does not bob or move, then the Sajda is correct and valid even on grass.
It is given in Radd Ul Muhtaar, Vol. 1, Pg. No: 370:
Translation: It is necessary that while performing the Sajda, one should feel the hardness of the surface, which means that when the person offers the Sajda nicely then his (or her) forehead should not go down more than where it was placed. For this reason, Sajda is not correct on a soft surface like a grass or a quilt. If one feels the hardness of the surface, then it is correct.
What to do if a Sajda is missed in Salaat
In every Raka’at, 2 Sajda are Fardh (obligatory) and are the articles of the Salaat. If any Fardh is delayed in the Salaat, then the Sajda Sahw (prostration on forgetfulness) becomes Wajib (compulsory) and if any Fardh is missed, then the Salaat is rendered invalid and should be offered again.
If any person performs only 1 Sajda in a Raka’at and goes for the next Raka’at, then if he/she remembers it in the next Raka’at, he/she should perform it before the Tashahud (At Tahiyyaat) i.e. he/she should offer 3 Sajda and should also perform the Sajda Sahw for delaying the Fardh.
If he/she remembers it after reciting the Tashahud, then he/she should perform 1 Sajda and should perform Sajda Sahw.
If he/she remembers it on ending the Salaat and has not turned the face away from the Qiblah and has not performed any other act, which breaks the Salaat then he/she should perform it then and also perform Sajda Sahw. As given in Fatawa A’alamgiri, Vol. 1, Kitab Us Salaat.
What makes Sajda Sahw Wajib:
Every mistake in Salaat does not make Sajda Sahw compulsory (Wajib).
Leaving any Masnoon (Sunnah) or Mustahab (Commendable) act does not make Sajda Sahw Wajib.
The following make Sajda Sahw Wajib:
Missing out on any Wajib act: like reciting Surah Fatiha, or another Surah after it, Tashahud, etc.
Distorting any Wajib act, like reciting softly in a Salaat in which the recitation is to be in a loud voice, delaying an article of Salaat, like reciting more than the "At Tahiyyaat" in the first Qaida (sitting) of the Salaat, which in turn delays the 3rd Raka'at.
Preponing any article of Salaat, like performing Sajda before Ruku, repetition of an article of Salaat like performing 3 Sajda in one Raka'at, in all these cases Sajda Sahw is compulsory.
If a person in the Salaat stays quiet for time enough to complete an act of Salaat, then it is called as delaying an act or delaying of compulsory article. The time equal to completing an act is mentioned as time enough for the recitation of three Tasbihaat (glorifications). Therefore, if a person keeps quiet for a period equivalent enough for the recitation of three glorifications (i.e. Subhana Rabbi A'ala or Subhana Rabbi Al Azeem or the like), then he/she should make the Sajda Sahw.
As given in Raddul Muhtaar, Vol. No. 1, Pg. No. 558
What if more than 1 mistake in the Salaat?
If in a Salaat, more than 1 mistake, which make Sajda Sahw Wajib occur, then only one Sajda Sahw will be enough for all.
Method of performing Sajda Sahw:
Please keep in mind that as per the Hanafi school of Fiqh, the method of Sajda Sahw as described in the Hadith is that after reciting "At Tahiyyat," one Salaam should be done on the right side, then 2 Sajda should be performed and then "At Tahiyyat," Durud Ibrahim and Dua Mathoora should be recited. As given in Fatawa A'alamgiri, Vol. 1, Pg No. 126 and Pg No. 130.