Our Master, the beloved Prophet Muhammad (sallal laahu alaihi wasallam) has said: In Paradise there is a castle reserved for those who read Tahajjud and the Prophet (sallal laahu alaihi wasallam) further adds, those who pray at night will enter paradise without having to account for their acts in this life.
The Nafils of Tahajjud are read after the Esha prayer, but it is important to sleep before performing Tahajjud. The prayer consists of a minimum of 2 Raka-ats, and a maximum of 8 or 12 Raka-ats (to be read according ones capacity).
After Esha prayers sleep for some time, then wake up any time during the night before the rise of morning for Tahajjud prayers. With the performance of 2 Rakats you have duly achieved your Tahajjud. However, the performance of 8 Rakats in Sunnat, and complying with the practice of the Holy Saints of Islam and performing 12 Rakats is commendable.
It is recommended that you recite in your prayers as much of the Sacred Quran as you know. If you happen to know by heart the whole of the Sacred Quran you may, in at least 3 nights or most 4 nights of Tahajjud effectuate the complete reading of the Sacred Quran.
Otherwise, you may recite 3 Surah Ikhlas (Qul Hu Allahu Ahad) after your "Alhamdu..." in every Rakat and you will thus derive full benefits of the full recital of the Sacred Quran in every Rakat.
During the month of Ramadan one should awake a little earlier for Sehri and make time to pray Tahajjud Salaah for the reward is magnified so much more in Ramadan and duas are even more readily accepted than at any other time of the year.
The dua's at the time of Tahajjud are very readily accepted by Almighty Allah and one should repent and ask of Allah and try to cry in their dua's at this time, if one cannot cry due to the hardness of ones heart due to sin then at least one should make the face as if one is crying. Just as a mother tends to her baby quickly and promptly when it cries the same way Allah attends to his servant quicker when they are crying.