Lailatul Raghaib' - First Thursday Night of Rajab

The first Thursday night of Rajab is considered significant, especially in making your relation with Allah stronger. Apart from the fast and prayer, scholars also recommend seeking Allah's pleasure by serving His creations.
The Holy Prophet (s.a) is reported to have said, that the prayers are Means of forgiveness and on the first night in our grave, the Almighty will send the reward of this prayer in the best, enlightened and eloquent form.
It is recommended to fast on the first Thursday of the Month of Rajab

A 12 Rakat Salat is recited between Isha and Midnight (However its popularly recited between Magrib and Isha) The Niyat/intention is to be of "Rija Matloob" and not as Mustahab(recommended )

Note : Though the salat is mentioned in Iqbal Amal , it is narrated by Anas bin Malik who was an adversary to the Ahlulbayt(as) and hence authenticity is not verified.
Some scholars mention instead recite Salaat Jafar Tayyar

The Method of the 12 Rak’at salaat is
Recited in six sets of 2 units.In every Rak’at after Surah al Hamd recite 3 times Surah al-Qadr and 12 times Surah Ikhlaas
After completing the full prayer :
Recite 70 times:
اَللَّهُمَّ صَلِّ عَلَىٰ مُحَمَّدٍ ٱلنَّبِيِّ ٱلامِّيِّ وَعَلَىٰ آلِهِ
Allahumma s’ale a’laa muh’ammadin nabiyyil ummi wa a’laa aaleh.
O Allah send blessings on Muhammad, the Ummi Prophet, and on his descendants.
Then go into sajdah & recite 70 times:
سُبُّوحٌ قُدُّوسٌ رَبُّ ٱلْمَلاَئِكَةِ وَٱلرُّوحِ
subbuh’un quddoos rabbul malaaaekate war-rooh’
Holy and most Holy is the Lord of the Angels and spirits.
Then sit erect and say 70 times:
رَبِّ ٱغْفِرْ وَٱرْحَمْ وَتَجَاوَزْ عَمَّا تَعْلَمُ إنَّكَ انْتَ ٱلْعَلِيُّ ٱلاعْظَمُ
rabbighfir war-ham watajaawaz a’mma ta’lamo innaka antal a’liyyul a’zam
O Lord! Forgive, have mercy and be indulgent about that which Thou knows well, verily Thou art Sublime, Mighty.
Then go into sajdah & say 70 times:
سُبُّوحٌ قُدُّوسٌ رَبُّ ٱلْمَلاَئِكَةِ وَٱلرُّوحِ
subbooh’un quddoos rabbul malaaekate war-rooh Holy and most Holy is the Lord of the Angels and spirits.

Watch this Video for a clarification on the salaat.