Allah Almighty says, "Allah and His angels call down blessings on the Prophet. O you who believe! Call down blessings on him and ask for complete peace and safety for him." (33:56)
Abdullah ibn Amr ibn al-Aas reported the Messenger of Allah sallallaahu alayhi wasallam says, "Anyone who sends prayer on me, Allah will send prayer on him ten times on account of it." [Muslim]
Ibn Masud stated that the Messenger of Allah sallallaahu alayhi wasallam said, "The nearest of people to me on the Day of Judgement will be the one who blesses me the most." [at-Tirmidhi]
Aws ibn Aws reported that the Messenger of Allah sallallaahu alayhi wasallam said, "The best of your days is the Day of Jumah (Friday), so do a lot of prayers on me during it. Your prayer is shown to me." The Companions asked, "O Messenger of Allah, how will our prayer be shown to you when you have become dust?" He said, "Allah has forbidden the earth to consume the bodies of the Prophets." [Abu Dawud]
Abu Huraira reported that the Messenger of Allah sallallaahu alayhi wasallam said, "May humiliation be the lot of any man who, when I am mentioned in his presence, does not pray for blessings on me." [at-Tirmidhi]
Abu Huraira reported that the Messenger of Allah sallallaahu alayhi wasallam said, "Your prayer reaches me wherever you are." [Abu Dawud]
Abu Huraira reported that the Messenger of Allah sallallaahu alayhi wasallam said, "No one greets me without Allah returning my spirit to me so that I can return the greeting to him." [Abu Dawud]
Ali reported that the Messenger of Allah sallallaahu alayhi wasallam said, "A miser is someone who, when I am mentioned in his presence, does not pray for blessings on me." [at-Tirmidhi]
Fadala ibn Ubayd said, "The Messenger of Allah sallallaahu alayhi wasallam heard a man making supplication in his prayer without glorifying Allah Almighty or praying for blessings on the Prophet. The Messenger of Allah sallallaahu alayhi wasallam said, 'This one was in a hurry.' Then he called him and said to him - or to someone else - "When one of you prays, he should begin by glorifying his Lord, glory be to Him! and praising Him, and then pray for blessings on the Prophet. Then he should ask for anything else he wants afterwards.'" [Abu Dawud and at-Tirmidhi]
Abu Muhammad Kab ibn Ujra said, "The Prophet sallallaahu alayhi wasallam came out to us and we said, 'Messenger of Allah, we know how to greet you, but how should we bless you?' He said, 'Say, "O Allah, bless Muhammad and the family of Muhammad as You blessed the family of Ibrahim. You are Praiseworthy, Glorious. O Allah, grant blessings to Muhammad and the family of Muhammad as You granted blessings to the family of Ibrahim. You are Praiseworthy, Glorious."' [Agreed upon]
(Riyad al-Saliheen, abridged)