The sunnah in the funeral prayer is that one says the takbir, then recites the opening surah of the Quran, then sends prayers upon the Prophet ﷺ, then makes sincere supplication for the deceased. He recites only after the first takbir, then gives the salam silently to his right.
السنة في الصلاة على الجنائز أن يكبر، ثم يقرأ بأم القرآن، ثم يصلي على النبي ﷺ، ثم يخلص الدعاء للميت، ولا يقرأ إلا في التكبيرة الأولى، ثم يسلم في نفسه عن يمينه.
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Narrated by Abdul-Razzaq (6428), and from his route Ibn Jarud in Muntaqa (540), from Mamar, from Zuhri, who said, "I heard Abu Umama bin Sahl bin Hunayf narrating to Ibn Musayab," and then he mentioned it. Its isnad is sahih. Ibn Qayyim also graded it sahih in Jala Afham (p. 193).Abu Umama is Asad bin Sahl bin Hunayf al-Ansari. He was born during the lifetime of the Prophet ﷺ but did not hear from him directly, so his narration from the Prophet ﷺ falls under the category of the companions' disconnected reports. This category is accepted by the consensus of the scholars.The hadith has other routes mentioned in the Book of Funerals.