There is a number of hadiths that confirm that the Prophet (peace and blessings be upon him) made du`aa’ after Salah. For example, Sa`d Ibn Abi Waqqas (may Allah be pleased with him) used to recommend these five (statements) and say that the Prophet (peace and blessings be upon him) said so (and they are): “O Allah! I seek refuge in You from miserliness, and I seek refuge in You from cowardice, and I seek refuge in You from being brought back to geriatric old age, and I seek refuge in You from the afflictions of the world, and I seek refuge with You from the punishment of the grave.” (Al-Bukhari, Sahih, vol. 8, hadith no. 381)
As for raising hands, there are also some hadiths which indicate that it is recommended to raise hands when making du`aa’.
The eminent Muslim scholar Sheikh `Abdel Khaliq Hasan Ash-Shareef, a renowned scholar and Da`iyah, stated:
“Du`aa’ is an essential act of worship. A Muslim should always be keen to make du`aa’ to Allah especially in good times such as the time after Prayers.
As for raising hands during supplication, it is authentic. Ibn Hajar mentioned that the Prophet (peace and blessings be upon him) raised his hands in 29 situations in du`aa’. In addition there is no proof that prohibits raising hands in du`aa’ after the obligatory prayer.”