The questioner asks: What is Sakeenah (tranquillity) and how does it descend upon the believers?
Sakeenah (tranquillity) is the calmness, relaxation and happiness a person feels inside his heart, and from the means of (experiencing) this Sakeenah and happiness in the heart is when one is constant in the remembrance of Allaah. Allaah (Glorified be He and free is He from all imperfections) said:
الَّذِينَ آمَنُوا وَتَطْمَئِنُّ قُلُوبُهُم بِذِكْرِ اللَّهِ ۗ أَلَا بِذِكْرِ اللَّهِ تَطْمَئِنُّ الْقُلُوبُ
Those who believe (in the Oneness of Allah – Islamic Monotheism), and whose hearts find rest in the remembrance of Allah, Verily, in the remembrance of Allah do hearts find rest. [13:28]
Ibnul Jawzi (rahimahullaah) said that two statements have been mentioned regarding the word Dhikr; one of them is that Dhikr means the Qur’aan and the second statement is that it means the remembrance of Allaah in general.
And with regards to the meaning of Tu’maneenah (repose or rest) there are two statements: The first one is that it is love of Allah and being completely at ease in His presence. The second meaning is that it is complete submission to Him without harbouring any doubts as opposed to those whose hearts are filled with disgust when Allaah is mentioned.
In summary: Constant remembrance of Allaah (through recitation of) the Qur’aan; remembering Him by uttering Subhaanallaah, Alhamdulil laah, Allaahu Akbar and thanking Him, sending the salaah and salaam upon His Prophet [Muhammad (sallal-laahu-alayhi-wasallam)], constantly repenting to Allaah and seeking His Forgiveness- all these deeds bring about Sakeenah (tranquility) in the heart of the believer. And Allaah knows best.
[Source: Fadaa’il Al A’maal’ pages 11-12’ by Shaikh Muhammad Bin Abdillaah As-Subayyil (rahimahullaah). Abridged and slightly paraphrased]