Reciting the Durood in salah is Sunnah according to the Hanafis and Malikis and a pillar according to the Shafi'is and Hanbalis. See What to say on the 4th rakat during fard or sunnah prayer
The minimum requirement according to the Shafi'is is to say:
اللهم صل على محمد وعلى آل محمد
And the minmum requirement according to the Hanbalis is to say:
اللهم صل على محمد
The recommended wording is what is commonly called the Durood of Ibrahim:
سألنا رسول الله صلى الله عليه وسلم فقلنا يا رسول الله كيف الصلاة عليكم أهل البيت فإن الله قد علمنا كيف نسلم. قال " قولوا اللهم صل على محمد، وعلى آل محمد، كما صليت على إبراهيم وعلى آل إبراهيم، إنك حميد مجيد، اللهم بارك على محمد، وعلى آل محمد، كما باركت على إبراهيم، وعلى آل إبراهيم، إنك حميد مجيد
We asked Allah's Messenger (ﷺ) saying, 'O Allah's Messenger (ﷺ)! How should one (ask Allah to) send blessings on you, the members of the family, for Allah has taught us to salute you?'
He said, 'Say: O Allah! Send Your Mercy on Muhammad and on the family of Muhammad, as You sent Your Mercy on Abraham and on the family of Abraham, for You are the Most Praise-worthy, the Most Glorious. O Allah! Send Your Blessings on Muhammad and the family of Muhammad, as You sent your Blessings on Abraham and on the family of Abraham, for You are the Most Praise-worthy, the Most Glorious.
— Bukhari
The madhabs adopt some variant of this report as the recommended wording.