How to pray Tahajjud Prayer. How many rakats are required and how many minutes before Fajr can you pray? Are nafl prayed at this time?

There is no difference between Tahajjud and Qiyam al-lail (the late-night prayer). If the prayer is performed after one had slept then it is called Tahajjud otherwise it is called Qiyam-al-lail. There are many evidences in Qur'an and Sunnah proving the excellence and merits of Tahajjud.

Allah Says,

“Is one who is devoutly obedient during periods of the night, prostrating and standing [in prayer], fearing the Hereafter and hoping for the mercy of his Lord, [like one who does not]? Say, "Are those who know equal to those who do not know?" Only they will remember [who are] people of understanding."[1]

 Allah Praises those who perform the late-night prayers,

"They arise from [their] beds; they supplicate their Lord in fear and aspiration, and from what We have provided them, they spend. And no soul knows what has been hidden for them of comfort for eyes as reward for what they used to do." [2]

Imam Tirmizi narrates from Abdullah ibn Salaam that,

"When the Prophet (ﷺ) came to Madinah, the people gathered around him and I was one of them. I looked at his face and understood that it was not the face of a liar. The first words I heard him say were: 'O people, spread the salutations, feed the people, keep the ties of kinship, and pray during the night while the others are sleeping and you will enter paradise in peace."' [3]

The Prophet (ﷺ) said:

"The best prayer after the obligatory prayers is the prayer which is performed in the last part of the night".[4]

Therefore, the night prayer is a confirmed Sunnah, its rule does not change even in the month of Ramadhan. However, performing it during Ramadhan is better than during other months.

The time of Tahajjud (Qiyam al-lail) starts after obligatory prayer of Isha and extends till dawn. There is no specific time for this prayer so it may be performed at any time of night but the preferred time is the last third of the night. There is no specific number of Rak'ah of this night prayer but the Prophet (ﷺ) never prayed more than thirteen Rak'ah during Ramadhan or any other time.

The Sunnah is to be performed in sets of two Rakah. It is recommended to shorten the first two Rak'ah making the remaining Rak'ah longer. And then one should end it with one Rak'ah of Witr. One may also make Dua' Qunoot in Witr if he likes. The person who does not memorize much Qur'an may recite many short Surahs in one Rak'ah or he may read looking in the Mus'haf too.

Allah knows best!

References:

[1] [Qur’an 39:9]

[2] [Qur’an 32:16-17]

[3] [Al-Hakim relates this, Ibn Majah, and at-Tirmidhi who calls it Hasan Sahih.]

[4] [Sahih Muslim, 1163; Jami` at-Tirmidhi, 438]