Salatul-Tasbeeh is not a recommended practice. It is rather a Mustahab practice. If one has the ability and opportunity to offer it then one may do so.
The method of performing Salatul-Tasbeeh is as below:
1- Make intention of offering four Rak'ah of Nafl Salah.
2- In your first Rak'ah, say Allah-O Akbar, recite Thana, Al-Fatiha, another Surah and then say the following the Tasbeeh 15 times before going into Ruku:
سبحان الله والحمدلله ولا إله إلا الله والله أكبر
3- In Ruku, after reading the regular Tasbeeh, say the above mentioned Tasbeeh 10 times.
4- In Qauma, after saying ربنا ولك الحمد say the above mentioned Tasbeeh 10 times.
5- In Sajdah, after reading the regular Tasbeeh, say the above mentioned Tasbeeh 10 times.
6- After getting up from first Sajdah, read the above mentioned Tasbeeh before going into second Sajdah.
7- Say the above mentioned Tasbeeh 10 times again after reading the regular Tasbeeh in second Sajdah.
8- After the second Sajdah's Takbeer, say the above mentioned Tasbeeh before you stand up to offer second Rak'ah.
In total this will be 75 times of Tasbeeh in each Rak'ah. In second and fourth Rak'ah you will have to recite the Tasbeeh before reciting Tashahhud.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America