Zikr (or dhikr) is remembrance of the Beloved whom is none other than God or Allah. The Hindus have a similar practiced called Smarana which also means "remembrance."
The first part of the Islamic shahadah, La ilaha ilAllah ("there is no god but God") can be repeated over and over as a form of Zikr. The name Allah by itself can also be used. On a misbaha (Islamic rosary usually of 33 beads) you can chant Alhamudlillah ("Praise God") 33 times, Subhanallah ("Glory be to God") 33 times, and then Allahu Akbar ("God is the Greatest") 33 times. Some people memorize the Asma ul-Husna or 99 Names of God and chant them as a form of Zikr. I think that some Muslims chant the 112th chapter of the Qur'an as a form of Zikr. Chapter 112, al-Ikhlas, is translated as "Say: He, God is One, God is Eternal. He does not beget, He is not begotten, and like Him there is not even one." The Arabic is qul hu allahu ahad allahu samad lam yalid wa lam yulad wa lamyaku lahu kufuwan ahad.
It is important to know that these practices of Zikr in Sufism are themselves Islamic practices. Zikr is explained in the Qur'an and in the Sunnah.. then it is a Sufi practice because Sufism is simply Islamic mysticism.
Zikr can be practiced at any time, in case you were wondering.
And most importantly, do you have an Islamic view of existence? If you do not believe in Qur'an nor adhere to Islam then you will probably have a hard time working with Sufis. But, who says you can't practice Zikr as a simple mystical practice? You can get wonderful results if you believe it works. It's like how anyone, Hindu or not, can do the Smarana practice of chanting the mantra Hare Krishna Hare Krishna Krishna Krishna Hare Hare Hare Rama Hare Rama Rama Rama Hare Hare and get good results.
I have descended, O my darling, into the black shining waters, and I have plucked Thee forth as a black pearl of infinite preciousness. - III:60 / Liber 65