Tirmidhi

Commentary:
1:
Apparently, this hadith is not related to "Salat al-Tasbih" but to general prayers, rather, in Musnad Abi Ya'la, the wording "obligatory prayer" is mentioned. Also, the method of tasbih mentioned in this hadith is not even present in Salat al-Tasbih.

Benefit No. 1: Shaykh al-Islam, the Imam, the Mujahid, Abdullah ibn al-Mubarak rahimahullah describes the method of Salat al-Tasbih as follows:
«يكبّر، ثمّ يقول: سبحانك اللّٰهمّ وبحمدك، وتبارك اسمك، وتعالي جدّك، ولا إله غيرك، ثمّ يقول خمس عشرة مرّة: سبحان اللّٰه، والحمد للّٰه، ولا إله إلّا اللّٰه، واللّٰه أكبر، ثمّ يتعوّذ، ويقرأ بسم اللّٰه الرحمن الرحيم، و فاتحة الكتاب، وسورة، ثمّ يقول عشر مرات: سبحان اللّٰه، والحمد للّٰه، ولا إله إلّا اللّٰه، واللّٰه أكبر، ثمّ يركع، فيقولها عشرا، ثمّ يرفع رأسه من الركوع، فيقولها عشرا، ثمّ يسجد، فيقولها عشرا، ثمّ يسجد الثانية، فيقولها عشرا، يصلّي أربع ركعات على هذا، فذلك خمس وسبعون تسبيحة فى كلّ ركعة، يبدأ فى كلّ ركعة بخمس عشر تسبيحة، ثمّ يقرأ، ثمّ يسبّح عشرا، فإن صلّى ليلا، فأحبّ إلى أن يسلّم فى الركعتين، وإن صلّى نهارا، فإن شاء سلّم، وإن شاء لم يسلّم .»

“The worshipper should say the takbir, then recite «سُبْحَانَكَ اللّٰهُمَّ», then recite this supplication fifteen times: «سُبْحَانَ اللّٰهِ، وَالْحَمْدُ لِلّٰهِ، وَلاَ إِلٰهَ إِلاَّ اللّٰهُ، وَاللّٰهُ أَكْبَرُ» (Allah is free from imperfection, all praise is for Allah, there is no deity except Him, and Allah is the Greatest), then recite ta‘awwudh and Bismillah, then Surah al-Fatihah and any other surah, then recite this supplication ten times, then bow (ruku‘) and recite this supplication ten times, then rise from ruku‘ and recite this supplication ten times, then prostrate (sujud) and recite this supplication ten times, then perform the second prostration and recite this supplication ten times, and in this manner complete four rak‘ahs. In each rak‘ah, there will be a total of seventy-five tasbihat. Each rak‘ah will begin with fifteen tasbihat, then recitation, then ten tasbihat. If Salat al-Tasbih is performed at night, it is preferable to say salam after two rak‘ahs, and if performed during the day, it is permissible to say salam or not; both are correct.

Hadith Reference: [سنن الترمذي، تحت حديث: 481، المستدرك للحاكم: 1/320، وسنده، صحيحٌ]

Benefit No. 2: ‘Allamah ‘Abd al-Hayy Lakhnawi al-Hanafi writes:

«اعلم أنّ أكثر أصحابنا الحنفيّة وكثير من المشايخ الصوفيّة، قد ذكروا فى كيفيّة صلاة التسبيح الكيفيّة الّتي حكاها الترمذيّ والحاكم عن عبد اللّٰه ابن المبارك الخالية عن جلسة الاستراحة، والمشتملة على التسبيحات قبل القرائة وبعد القرائة، وذلك لعدم قولهم بجلسة الاستراحة فى غيرها من الصلوات الراتبة، والشافعيّة والمحدثون أكثرهم اختاروا الكيفيّة المشتملة على جلسة الاستراحة، وقد علم ممّا أسلفنا أنّ الأصحّ ثبوتا، هو هذه الكيفيّة، فليأخذ بها من يصلّيها حنفيّا كان أو شافعيّا .»

“Know that most of our Hanafi companions and many Sufi shaykhs have mentioned the method of Salat al-Tasbih as narrated by Imam Tirmidhi and Imam Hakim from Imam Abdullah ibn al-Mubarak. This method does not include the sitting of rest (jalsat al-istirahah) and consists of tasbihat before and after the recitation. Most of the Hanafis have adopted this method because they do not consider the sitting of rest in regular prayers, whereas the Shafi‘is and most of the hadith scholars have preferred the method of Salat al-Tasbih in which the sitting of rest is present. From our previous discussion, it has become clear that the more correct method is the one with the sitting of rest. Whoever performs Salat al-Tasbih, whether Hanafi or Shafi‘i, should adopt this (method with the sitting of rest).” (al-Athar al-Marfu‘ah fi’l-Akhbar al-Mawdu‘ah by ‘Abd al-Hayy: 141)

Benefit No. 3: Imam ‘Abd al-‘Aziz ibn Abi Rawzah says that Imam Abdullah ibn al-Mubarak rahimahullah said:
«يبدأ فى الركوع، سبحان ربّي العظيم، وفي السجود، سبحان ربّي الأعلي ثلاثا، ثمّ يسبّح التسبيحات .»

“The one performing Salat al-Tasbih will first recite ‘Subhana Rabbiyal ‘Azim’ three times in ruku‘, and in sujud will first recite «سبحان ربّي الأعلي» three times, then will recite the tasbihat of Salat al-Tasbih.” (Sunan al-Tirmidhi, under Hadith: 481, and its chain is sahih)

Benefit No. 4: He also says that I asked Imam Abdullah ibn al-Mubarak rahimahullah: If the worshipper forgets, should he recite the tasbihat ten times in the prostration of forgetfulness (sujud al-sahw) as well? He rahimahullah replied: «لا، إنّما هي ثلاثمائة تسبيحة .»

“No, there are only three hundred tasbihat (in the four rak‘ahs).” (ibid., and its chain is sahih)

Warning: To perform Salat al-Tasbih in congregation is an innovation (bid‘ah), because it is not established from the Prophet sallallahu alayhi wa sallam that it was performed in congregation. Only those voluntary prayers (nawafil) whose congregation is established from the Sunnah should be performed in congregation; otherwise, even the regular Sunnah prayers (sunan al-rawatib) should be allowed in congregation, whereas no Muslim has ever done so until today.

1300. Commentary: In the mentioned hadith, it is not stated anywhere that this remembrance (dhikr) should be done after the tashahhud; in other narrations, it is explicitly mentioned that this remembrance is to be done after the salam (concluding salutation). (See, Hadith: 1349) Or, in the phrase (What supplication should I make in my prayer? [فِي صَلَاتِي]), the word "salat" may be taken to mean supplication (du'a). The meaning would then be: Teach me such words that I may recite in my supplication. The response of the Messenger of Allah (sallallahu alayhi wa sallam) supports this interpretation. The inference of Imam al-Nasa'i rahimahullah (that this remembrance is before the salam) is open to question; rather, this remembrance is also after the prayer, and supplication after remembrance is also after the prayer. And Allah knows best.