The word Dhikr is Arabic for “Remembrance”. Qur’an identifies that Dhikr or “Remembrance” is the memorization and recitation of the Book of Allah:
ذَٰلِكَ نَتْلُوهُ عَلَيْكَ مِنَ الْآيَاتِ وَالذِّكْرِ الْحَكِيمِ
“This We recite to you of the signs and the Wise Remembrance.” 3:58
This verse shows that (a) it is Qur’an which is Dhikr of Allah, and (b) it is a recitation. Another ayah identifies Dhikr:
إِنَّا نَحْنُ نَزَّلْنَا الذِّكْرَ وَإِنَّا لَهُ لَحَافِظُونَ
“Surely We, Ever We, have been sending down the Remembrance, and surely We are indeed Preservers of it.” 15:9
This verse shows that Dhikr is revealed by Allah. In other words the rememberance of the Qur’an, and the fact that it will be preserved by Allah in human memory in all times.
Some people think that Dhikr of Allah is done by chanting the names of Allah a certain number of times. However along with identifying what is Dhikr, Qur’an also shows how it is to be done, as this verse shows:
فَاذْكُرُوا اللَّهَ كَذِكْرِكُمْ آبَاءَكُمْ أَوْ أَشَدَّ ذِكْرًا
“..then remember Allah like the remembrance of your fathers or (even) with stronger fervor in remembrance.” 2:200
The command given about Dhikr Allah is that it should be done as we do the remembrance of our fathers and ancestors or even greater than that. We do not merely chant the names of our ancestors gone by over and over again on beads when we remember them, but remember them by recalling their deeds, and events of their life. In the same manner we have to remember Allah not just by chanting His name over and over again but by reciting His commandments, and the events that He has described in His Book. in other words we remember Allah by remembering His words i.e. the Qur’anic ayaat.
If we remember Allah in this manner, i.e. by remembering Quranic verses, orders and events, and specially those that relate to our life and the problems we face (keeping in mind that Qur’an has all guidance for any matters effecting our personal lives), the result will be as described in the following verse:
الَّذِينَ آمَنُوا وَتَطْمَئِنُّ قُلُوبُهُم بِذِكْرِ اللَّهِ- أَلَا بِذِكْرِ اللَّهِ تَطْمَئِنُّ الْقُلُوبُ
“Those who believe, and whose hearts find satisfaction in the remembrance of Allah: for without doubt in the remembrance of Allah do hearts find satisfaction.” 13:28
So if you want tranquility in your hearts, then believe in the Qur’an, study and memorise its verses, specially those that relate to the problems in your life, and remember and recite them often. By doing this you will be engaging in Dhikr Allah as instructed by Allah Himself, in His Book and attain satisfaction in your heart.