It is recommended to supplicate often during all times, especially during the month of Ramadan, in the last ten nights, and during the odd nights of it even more so. It is recommended that one say the following supplication a lot:
"O Allah! Verily, you are the Oft-Pardoning, You love to pardon, so pardon me."
"Allaahumma Innaka 'Afuwwun Tuhibbul-'Afwa Fa'affoo 'annee."
This is due to what Imam Ahmad recorded from Aishah that she said "O Messenger of Allah! If I find the Night of Al-Qadr what should I say?" He (saws) replied,
Say : "O Allah! Verily You are the Oft-Pardoning, You love to pardon, so pardon me."
At-Tirmidhi, An-Nasai and Ibn Majah have all recorded this Hadith . At-Tirmdhi said "This Hadith is Hasan Sahih" . [Tahfat Al-Ahwadhi 9:495, An-Nasai in Al-Kurba 6:218, and Ibn Majah 2:1265]
Al-Hakim recorded it in his Mustadrak (with a different chain of narration) and he said that it is authentic according to the criterial of the two Shaykhs (Al-Bukhari and Muslim).
[Al-Hakim 1:530] An Nasai also recorded it. [An-Nasai in Al-Kubra 6:219]