Prophet (صلی اللہ علیہ وسلم) said that when you see the moon of Rajab then first recite the following dua once:

Nafl prayer:
In the month of Rajab after praying the Isha Namaz on the first night pray 10 rakat namaz with the action of salam five times. In each rakat after reciting surah Fatiha recite surah Kafaroon I three times and surah Ikhlas three times as well. Inshallah, Allah Almighty will grant him the status of a martyr on the Day of Judgment and also increase his status considerably.

First night:
After praying the Isha Namaz prays four rakats with the action of salam two times. After each rakat after reciting surah Fatiha recite surah Alam Nashrah, surah Ikhlas, surah Falaq and surah Nas once. After saying the salam of two rakat recite the Kalma Tauheed and Darood Shareef 33 times. Then pray two rakat just like those prayed before and once again recite Kalma Tauheed and Darood Shareef 33 times after which pray for whatever you want, Insha’Allah Allah Almighty will grant your prayer. 
In the month of Rajab after praying the Isha Namaz on Friday pray two rakat. In the first rakat after reciting surah Fatiha recite surah Baqarah's last two ayats 7 times ( -----  ) . Then in the two rakats recite surah Hashr's last ayaat 7 times () . After saying the salam pray for whatever you want to be granted. Inshallah Allah Almighty will accept your wishes. This prayer is very effective for every kind of wish. 
In this month after praying the Maghrib Namaz on Friday pray 12 rakat nafl with the action of salams six times. In each rakat after reciting surah Fatiha recite surah Qadr 3 times and surah Ikhlas 12 times. Then recite () 70 times. Then prostrate and recite                            ( )70 times. After straightening recite

70 times and then do the second prostration in the same way. After this whatever prayer you ask for will be accepted.

27th Night:
In the month of Rajab, on the the 27th night pray 12 rakat namaz with the action of salam 3 times. In the first four rakat after reciting surah Fatiha recite surah Qadr in each rakat three times. After saying the salam recite the following verse () 70 times. In the second four rakat after reciting surah Fatiha recite surah Nasar three times in each rakat. After saying the salam recite the following verse ()70 times. In the third four rakat after reciting surah Fatiha recite surah Ikhlas three times in each rakat. After saying the salam recite surah Alam Nashrah 70 times then pray to Allah Almighty. Inshallah He will give whatever you asked for. In this month, on the fifteenth, after any prayer, to recite the following verses of Istagfar is quite effective as Allah will remove all of a person's wrongdoings and replace them will good deeds instead:

In this month on any day after praying the Duhr or Maghrib or Isha Namaz to recite surah Kahf, surah Yaseen, surah Ha Mim, surah Duhan and surah Maarij once and then reciting surah Ikhlas one thousand times, Allah Almighty will grant a special reward to the person.