13th, 14th and 15th of Rajab, Sha’aban and Ramadhan are known as “The Bright Days”. Imam Jafar Sadiq (a.s) had said: "Who prays during the nights of “The Bright Days”, in fact, stands at the door of superabundant favors, bounties and benefits available in these months".
1- It is highly desirable to observe fast on 13, 14 and 15, have a bath each day, and give alms in the way of Allah.
2- In the night of “The Bright Days” pray a 12 units Prayer as under
(i) In the night of the 13th pray 2 units:
In each unit recite Surah Hamd (The Opening), Surah Al Yaa Seen, and Surah Al Mulk (Dominion).
(ii) In the night of the 14th pray 4 units: in 2 sets of 2 units, each exactly as (i),
(iii) In the night of the 15th pray 6 units: in 3 sets of 2 of 2 units, each exactly as (i),
3- In the night of 15th:
(i) Recite Ziyaraat of Imam Hussein (a.s)
(ii) Pray the following 12 units prayer in 6 sets of 2 units each:
In every unit recite:
Soorah Al Faatih’ah 4 times
Soorah Al Ikhlaas 4 times
Soorah Al Falaq 4 times
Soorah Al Kaafiroon 4 times
Soorah Al Naas 4 times
Soorah Al Qadr 4 times
Ayatul Kursi 4 times
Tasbihaat ul Arbaa’ 4 times
After every Salaam recite 4 times:
Allah! Allah! My Lord! I associate not anything with Him. I choose no protecting friend beside Him. That which Allah wills (come to pass). There is no might and no strength save in Allah, the Hightest, the Almighty
4- On the 15th day:
(i) Pray Salman Farsi prayer. A 10 units prayer. Pray in 5 sets of 2 units each. In every unit recite Surah Hamd (The Opening) once, Surah Ikhlaas (The Purity)3 times & Surah Kafiroon ( the disbelievers) 3times.
Then after salaam raise both your hands towards the sky & recite:
There is no god save Allah, no one other than him; sovereignty belongs to HIM. all praise is for HIM alone, gives life, puts to death,(because)HE is ever living ,Immortal; in His hand is the good, He is able to do all thing
O my Allah there is no obstacle when thou gives, and there is no access to anything when thou puts a stop; there is no profit in exerting ones self in a matter when thou “looks the other way” & recite the following:
The one true God! Single! Unique! The eternally besought! He did not choose any associate nor a son.
(ii) Recite Ziyaraat of Imam Hussein (a.s) & this Special Ziyaraat
(iii) Pray 4 units prayer in 2 sets of 2 units each.
After Salaam recite the following supplication:
O my Allah! O He who puts the proud tyrants to shame! O He who glorifies the faithful! Thou was my choice at once when I came across many schools of thought (religions), Thou brought me into existence, a favor to me, though Thou was able to dispense with my creation, not needing me at all.
If not for Thy mercy I am of those who perish. Thou makes available reliable support to have an upper hand over my adversaries. If not for Thy help I am of those who shatter and break into pieces.
O He who sends forth mercy from its permanent self-generating origin, and brings out blessing from its depository.
O He who has reserved for Himself that which is the highest, and the loftiest, so His intimate friends, on account of His might, vie in honor and glory. O He before whom bend low the rulers, their necks burdened with the yoke of disgrace and abasement, panic-stricken, scared stiff, in awe of His absolute power.
I beseech Thee in the name of Thy Supreme Being that derives its meaning from Thy timeless eternal greatness, I beseech Thee in the name Thy timeless eternal Greatness that derives its meaning from Thy omnipotent authority; I beseech Thee in the name of Thy omnipotent authority with which Thou occupied the Arsh, and created all that which has been created by Thee; so they, unto Thee, are very obedient, to send blessing on Muhammad and on the people of his house.
* Source: duas.org