The integrals within the prayer are:
The opening takbeer (tahreema)
Standing
Reciting
Bowing
Prostrating
The final sitting
The tahreema is opening phrase 'Allahu akbar'. The place of it is on the tongue, i.e. it must be uttered such that one would hear himself in a quiet room. It must coincide with the intention in the heart, in other words there should be no unrelated activities separating the intention and tahreema.
Standing is obligatory for fard and wajib prayers.
Standing is defined as a position in which if one were to extend his arms towards his knees, they would not reach them. If one is physically unable to stand, then he should pray sitting on the floor.
Recitation of Quran even if one verse in the first two rakaat of the fard prayers and in all rakaat of other prayers. The Quran must be recited in the standing position, and, similarly to tahreema, it must be uttered such that one would hear himself in a quiet room. If one is a follower in a congregation, then he does not recite Quran as the recitation of the imam is counted for the whole congregation.
Bowing means bending one's back such that if one were to extend the arms towards knees, they would reach them. The minimum duration for bowing is the time it takes to say one tasbeeh, i.e. the phrase 'subhan Allah'.
Prostrating is placing one's forehead, two hands, two knees, and bottom of the toes of both feet on the ground. Both prostrations in every rak'ah are obligatory.
The place of prostration must bear the weight of the head, so one cannot prostrate on a surface that is too soft where the forehead is only touching. The place of prostration must also be relatively level, as the forehead cannot be significantly above the toes. Scholars say that more than 25cm is problematic.
The final sitting must be at least of duration it takes one to recite tashahhud. This sitting is final, therefore it must be performed after all other integral actions to be valid.
These integral are the essential actions within prayer, that together with conditions (shurut) constitute the fard elements of prayer. These fard elements are the bare minimum. Omitting any of it intentionally or out of forgetfulness makes one's prayer invalid.
Apart from the fard, one needs to also know wajib. Wajib is also obligatory, but omitting it out of forgetfulness can be rectified.