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How to Pray Tahajjud and Witr

The Witr Prayer 

"The Witr prayer is offered in units of two raka'at. If you fear that dawn is near, conclude with a single rak'ah so the night prayer will be of an odd number." (Bukhari) 

The Witr prayer is the last prayer of the night. It can be offered any time after Isha and before Fajr. hence why if you plan on praying Tahajjud you will wait to pray your Witr prayer after finishing your Tahajjud salah. Even though this is an extra prayer the Prophet (PBUH) would never leave it, even when he was traveling.   

The Witr Salah is done by praying two rak’ahs and then praying one single ra’kah. You can pray up to eight rak’ah, and then end it with one single rak’ah. Praying 3, 5, 7, and 9 ra’kah for witr salat is permissible. Another (Hanafi) method of praying this extra prayer is by praying three rak’ahs and then in the third ra’kah after reciting the surah, raise your hands in supplication, and recite Dua Qu’noot.     

in Arabic

اَللَّهُمَّ إنا نَسْتَعِينُكَ وَنَسْتَغْفِرُكَ وَنُؤْمِنُ بِكَ وَنَتَوَكَّلُ عَلَيْكَ وَنُثْنِئْ عَلَيْكَ الخَيْرَ وَنَشْكُرُكَ وَلَا نَكْفُرُكَ وَنَخْلَعُ وَنَتْرُكُ مَنْ ئَّفْجُرُكَ اَللَّهُمَّ إِيَّاكَ نَعْبُدُ وَلَكَ نُصَلِّئ وَنَسْجُدُ وَإِلَيْكَ نَسْعأئ وَنَحْفِدُ وَنَرْجُو رَحْمَتَكَ وَنَخْشآئ عَذَابَكَ إِنَّ عَذَابَكَ بِالكُفَّارِ مُلْحَقٌ

Allahumma ihdini feeman hadayt, wa a’fini fiman afait, wa tawallani fiman tawallait, wa barik Li fima atait, wa qini sharra ma qadait, fa Innaka taqdi wa la yuqda Alaik, wa innahu la yadhillu man walait, [wa la yaizzu man adayt], tabarakta Rabbana wa ta’alait.

Meaning

O, Allah! We invoke you for help and beg for forgiveness, and we believe in you and have trust in you and we praise you, in the best way we can; and we thank you and we are not ungrateful to you, and we forsake and turn away from the one who disobeys you. O, Allah! We worship you and prostrate ourselves before you, and we hasten towards you and serve you, and we hope to receive your mercy and we dread your torment. Surely, the disbelievers shall incur your torment

From that it is clear that the Sunnah with regard to tahajjud and Witr includes several things:

The worshipper should offer his prayers two (rak‘ahs) by two, so he should separate each two rak‘ahs of his prayer with the taslim.

He should start with tahajjud first, and pray as much as Allah wills that he should pray.

Witr should be the last of his prayers at night. The Prophet (blessings and peace of Allah be upon him) said: “Make the last of your prayers at night Witr (lit. odd-numbered).” (Narrated by al-Bukhari (953) and Muslim (751).

The worshipper should not delay any of his tahajjud or Witr until the break of dawn; rather he should try to make sure that he has done all of that before the adhan of Fajr.

An-Nawawi (may Allah have mercy on him) said:

“The words of the Prophet (blessings and peace of Allah be upon him),” then if one of you fears that dawn may come, he should pray one rak‘ah, which will make what he has prayed odd-numbered” – and according to another hadith, he said, “Pray Witr before dawn” – indicates that the Sunnah is to make Witr the last of the prayers offered at night, and that the time for it ends with the break of dawn. This is the well-known view in our madhhab, and it is the view of the majority of scholars. It was also said that the time lasts after dawn has broken, until the obligatory prayer is offered.” (Sharh Sahih Muslim, 6/30-32)

السلام و علیکم ورحمتہ اللہْ

May Allah help us all. Remember me and the entire Muslim Ummah in your Duas.
Allah' slave.