For Tahajjud prayer, it is essential to sleep and then wake up.
On awakening for Tahajjud prayer, the Holy Prophet(sa) would clean his teeth with the miswak (Sahih Bukhari, The Book of Tahajjud) and perform the ablution.
The Holy Prophet(sa) offered Tahajjud prayers in various ways – sometimes he would offer it in sets of two rak’aat and at other times he would offer four rak’aat at a time. Sometimes he would offer some rak’aat briefly, with short recitations and at other times he would prolong them. At times the prophet would offer some Tahajjud, go to sleep, then awaken and after performing ablution again, he would resume Tahajjud prayer.
For Tahajjud, the Holy Prophet(sa) would offer eight sets of two rak’aat and then the Witr prayer – totalling eleven rak’aat. He would at times offer two sets of four rak’aat and the Witr prayer. It is also mentioned in the ahadith that he would sometimes offer a set of two more rak’aat after the Witr prayers – totalling 13 rak’aat.
The Holy Prophet(sa) would offer Tahajjud prayer sometimes in the early part of the night, sometimes in the middle and also during the latter part of the night. There are various narrations.
We know from the ahadith that the Holy Prophet(sa) would also lay down, close his eyes and sleep a little after offering Tahajjud prayers until the Azan for Fajr was called.
If someone has not read their Witr prayers, they should offer them at Tahajjud, at the end, to make their Tahajjud an odd number. The Holy Prophet(sa) said:
مَنْ صَلَّى مِنَ اللَّيْلِ فَلْيَجْعَلْ آخِرَ صَلاَتِهِ وِتْرًا قَبْلَ الصُّبْحِ كَذَلِكَ كَانَ رَسُولُ اللَّهِ صلى الله عليه وسلم يَأْمُرُهُمْ
“He who observed the night prayer [Tahajjud] should make Witr the end of his prayer before dawn.” (Sahih Muslim, The Book of Prayers, Travellers)