Short answer
The Prophet ﷺ told us to send abundant salawat on him on Friday, because it is the best of days and our salawat are shown to him. There is no fixed number in authentic hadith, so send as much as you can. Durood Ibrahim is the best wording, and short forms are fine too.
Sending durood is mustahabb at all times and more so on Friday and its night (Thursday night). Reports fixing eighty durood after Asr on Friday are weak, so no number is required.
The four schools agree on this.
Explanation
Aws ibn Aws narrated that the Prophet ﷺ said: among the best of your days is Friday. On it Adam was created and on it he died, on it the Trumpet will be blown. So send much salawat on me on it, for your salawat are presented to me. The Companions asked how, when his body would have decayed, and he said Allah has forbidden the earth to consume the bodies of the prophets.
Why Friday? Friday is the weekly festival of the Muslims, the day of Jumu'ah and of an hour in which dua is answered. Linking it to salawat joins the best of days with one of the best of deeds. Allah Himself and His angels send blessings on the Prophet ﷺ, and the believers are commanded to do the same (33:56).
How much and when. No sound hadith sets a number. Some people read a hundred or a thousand, and a weak report mentions eighty after Asr; any number is fine as long as you do not believe it is a fixed sunnah. Scholars include Thursday night, since the Islamic day begins at sunset. Spread it through the day: on the way to Jumu'ah, after Asr, and when you hear his name in the khutbah (in your heart, without speaking, since the khutbah must be listened to in silence).
Which wording? Durood Ibrahim, which we read in salah, is the best. Short forms such as Allahumma salli 'ala Muhammad, or sallallahu 'alayhi wa sallam, are also salawat. See the shortest durood, the benefits of salawat and the sunnahs of Friday.
The evidence
Quran, Surah Al-Ahzaab 33:56
إِنَّ ٱللَّهَ وَمَلَٰٓئِكَتَهُۥ يُصَلُّونَ عَلَى ٱلنَّبِىِّ ۚ يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ صَلُّوا۟ عَلَيْهِ وَسَلِّمُوا۟ تَسْلِيمًا ﴿٥٦﴾
Indeed, Allah confers blessing upon the Prophet, and His angels [ask Him to do so]. O you who have believed, ask [Allah to confer] blessing upon him and ask [Allah to grant him] peace.
The command to send salawat on the Prophet ﷺ.
Sunan Abi Dawud 1047
Grading to be checked... فأكثروا علي من الصلاة فيه فإن صلاتكم معروضة علي ...
"So send much salawat on me on it, for your salawat are presented to me."
The command to increase salawat on Friday.
Sahih Muslim 408
Sahih... من صلى علي واحدة صلى الله عليه عشرا ...
"Whoever sends one salah on me, Allah sends ten on him."
The reward of every single durood.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, discussion of salawat on the Prophet after the tashahhud. Explains when salawat is fard, wajib and mustahabb, including on Friday.
- al-Adhkar (al-Nawawi), Chapter on salawat on the Prophet. Mentions increasing salawat on Friday and its night.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.