When the Messenger of Allah ﷺ stood for prayer, he would say the takbir as he stood up, then say the takbir when he bowed. When he raised his back from the bowing position, he would say, "Allah hears whoever praises Him." Then, while standing, he would say, "Our Lord, to You be all praise."Then he would say the takbir as he descended into prostration, then say the takbir when he raised his head, then say the takbir when he prostrated again, then say the takbir when he raised his head once more. He would do this throughout the entire prayer until he completed it, and he would say the takbir when he rose from the sitting position after the second rakah.
أخبرنا محمد بن رافع قال حدثنا حجين وهو ابن المثنى قال حدثنا ليث عن عقيل عن ابن شهاب قال أخبرني أبو بكر بن عبد الرحمن بن الحارث بن هشام أنه سمع
كان رسول الله ﷺ إذا قام إلى الصلاة يكبر حين يقوم ثم يكبر حين يركع ثم يقول سمع الله لمن حمده حين يرفع صلبه من الركعة ثم يقول وهو قائم ربنا لك الحمد ثم يكبر حين يهوي ساجدا ثم يكبر حين يرفع رأسه ثم يكبر حين يسجد ثم يكبر حين يرفع رأسه ثم يفعل ذلك في الصلاة كلها حتى يقضيها ويكبر حين يقوم من الثنتين بعد الجلوس
Muslim narrated it in the Book of Prayer, in the chapter on establishing the takbir at every lowering and rising in prayer, etc., hadith 29/392, from Muhammad bin Rafi. Bukhari narrated it in the Book of Adhan, in the chapter on the takbir when rising from sujud, hadith 789, from the hadith of Layth bin Saad, with the same chain. It is also found in Al-Kubra, hadith 736.