The month of Dhu’l-Qa`dah (Zilqad) is the first of the Sacred Months to which Almighty Allah has referred in the Holy Qur'an. Sayyid Ibn Tawoos defines this month as the month of responding to the prayers in hardships.
It is narrated from the Holy Prophet (Peace be upon him and his progeny) that it is recommended to offer this salaat on Sunday in the month of Dhil Qa'da .Reference Mafateeh Al Jinan by Shiekh Abbas Qummi

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Benefits of this salaat in narrations:-
-Sins will be forgiven and repentance will be accepted.
-Allah (swt) will make liabilities to others cleared and when will die with faith (Iman).
-Religion will be intact. Grave will be widened and enlightened.
-Parents will be pleased and Allah (swt) will forgive parents and children and will give more wealth.
-The Angel of Death will be gentle when taking the soul.

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It is recommended to do Ghusl & Wudhoo ( only Ghusl is insufficient)
Recite a 4 rakat ( 2 X 2) Salaat on any /all Sunday's in Zilqaad month. at any time during the day.
In every Unit/Rakat recite :
Sura Fatiha/Al Hamd x 1
Sura Ikhlass x 3
Sura Falaq x 1
Sura Naas x 1

After Salaam 70 times Istigfaar saying,

أَسْتَغْفِرُ اللّهَ وَأَتُوبُ إلَيْهِ.

astaghfiru allaha wa atubu ilayhi

I seek the forgiveness of Allah and I repent before Him.

Then once

لاَ حَوْلَ وَلاَ قُوَّةَ إِلاَّ بِٱللَّهِ ٱلْعَليِّ ٱلْعَظِيمِ

la hawla wala quwwata illa billahil aliyy'al azeem

There is no power and no strength except with Allah, the Most High, the All-great.

Then once

يَا عَزِيزُ يَا غَفَّارُ ٱغْفِرْ لِي ذُنُوبِي وَذُنُوبَ جَمِيعِ ٱلْمُؤْمِنِينَ وَٱلْمُؤمِنَاتِ

Ya azeezu ya ghaffar ighfir le dhunubi wa dhunuba jameea al mumeneena wal mumnenaati

O Almighty! O All-forgiving!(Please) forgive my sins and the sins of all believing men and women,

فَإِنَّهُ لاَ يَغْفِرُ ٱلذُّنُوبَ إِلاَّ انْتَ

Fa inna hu la yaghfiru aldhunuba illa anta

for none can forgive sins save You.

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From the 1st of Zilqada to 10th of Zilhijja are also the days of Arbaeen-e-Kalimiyyah.
These are the forty days when Nabi Musa (as) went on Mount Tur for Munajat from Allah (swt).
Initially it was to be for 30 days, another 10 days were added to make it 40 days as mentioned in Sura A’araaf - Aayat 143. During these days recitation of 'laa ilaaha illallaah ' is mustahab and very much stressed. (Source: Tazkiye Nafs by Ayatullah Misbah Yazdi)

Fasting for 3 Consecutive days Thursday Friday & Saturday has immense rewards in months of Zilqad, Zilhajj, Moharram