وَمِنَ اللَّيْلِ فَسَبِّحْهُ وَأَدْبَارَ السُّجُودِ
From the provided explanation: Use the nighttime for Tasbeeh, and declare Allah’s perfection on the backs of the sujood (i.e., at the end of the prayer when prostration is the last main act).
سَبِّحْ (Sabbih) is the command form from سَبَّحَ (Sabbaha) and تَسْبيح (Tasbeeh), which means to declare Allah’s perfection whilst keeping constantly in mind the opposite.
By declaring Allah’s perfection, you are acknowledging your own and everything else’s imperfection. Just like when you declare Allah’s greatness, you are acknowledging your own insignificance.
Use the nighttime to declare Allah’s perfection and flawlessness.
Quiet reflection and TasbeehDeclare Allah’s perfection on the backs of the sujood — at the end of the prayer when prostration is the last main act.
Post-prayer TasbeehIt was related from Abu Hurairah concerning the Messenger of Allah ﷺ: That they said: “O Messenger of Allah, the people of abundant wealth have made away with the highest degrees and the permanent pleasures”. He said: “How is that?” They said: “They pray as we pray, and strive in Jihad as we do, and spend from their surplus wealth in charity, while we have no wealth (to spend likewise)”. He said: “Shall I not tell you a thing, by doing which, you will catch up with those who are ahead of you and supersede those who will come after you; and nobody will be able to do such as you do except the one who does the same (deed as you do). To say SubhaanAllah ten times, and Al-Hamdu Lillah ten times, and Allahu Akbar' ten times after every prayer”.
This narration supports the reference to Tasbeeh after Salah.
Declaring Allah’s perfection entails acknowledging our own and everything else’s imperfection.
Declaring Allah’s greatness entails acknowledging our own insignificance.
Imperative to declare Allah’s perfection — the act of Tasbeeh.
Placement: at the end of the prayer when prostration is the final main act.