Almighty Allah says: "Surely Allah and His angels send blessings on the Holy Prophet (sallaLlahu ‘alaihi wa sallum). O you who believe! send blessings (durood) and salutations (salaams) on the Prophet with worthy salutation". (Surah al-Ahzab: 56) 

اللهم صلي و سلم و بارك علي محمد و صلي علي اله محمد

Narrated by Ubayy ibn Ka'b (Radi Allah Ta'lah Anhu): "I said: Allah's Messenger (SallaLlaho-alaihi-wasallum), I invoke blessings upon you very frequently. How much of my supplication should I devote to you. He said: As much as you like. I said: May it be a quarter? He said: As much as you like, but if you increase it, it will be good for you. I said: May it be a half? He said: As much as you like, but if you increase it, it will be good for you. I said: May it be two thirds? He said: As much as you like but if you make an increase in it, it will be better. I said: May I devote the whole of my supplication to you (that I make in my prayer)? Thereupon he said: In that case it will take care of you and your sins would be expiated."

Tirmidhi transmitted it. Hadith No. 929 of Mishkat al-Masabih

اللهم صلي و سلم و بارك علي محمد و صلي علي اله محمد

Sending peace and blessings on Fridays has been especially emphasized. Narrated Abu Darda (radiAllahu anahu) that The Prophet (salAllahu alayhi wasalam) said: 'Invoke blessings on me abundantly on the day of Jum‘ah (Friday) for it is witnessed. The angels attend it, and none invokes blessings on me but his supplication is presented to me till he stops.' I asked whether that applied also after his death, and he replied, 'Allah has prohibited the Earth from consuming the bodies of the prophets; so Allah's prophets are alive and given provision..'
[Ibn Majah no.1366 Mishkat al-Masabih]

اللهم صلي و سلم و بارك علي محمد و صلي علي اله محمد

There are also severe warnings for not sending prayers and blessings such as miser / dust on face when Muhammad (sallaLlahu ‘alaihi wa sallum) name is mentioned.

اللهم صلي و سلم و بارك علي محمد و صلي علي اله محمد