Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
One must begin tawaf (circumambulation) with one’s right shoulder uncovered, (for men only) and the Ka`bah on one’s left side, while facing the Black Stone, which you should kiss, if possible, touch with one’s hand, or point in its direction.
In this regard, in his well-known book Fiqh As-Sunnah Sheikh Sayyed Sabiq states:
1- One must begin tawaf (circumambulation) with one’s right shoulder uncovered, (for men only) and the Ka`bah on one’s left side, while facing the Black Stone, which you should kiss, if possible, or touch with one’s hand, or point in its direction, saying,
Bismillah wallahau akbar Allahumma imanan bika wa tasdiqan bikitabika wa wafa’an bi `ahdika wa ittiba`an li sunnati nabbiyyi sallalahu `alaihi wa sallam
(In the Name of Allah. Allah is the Greatest. O Allah! [I begin this tawaf] believing in You, affirming the truth of Your Book, fulfilling my covenant with You, and following the example of the Prophet, (peace and blessings be upon him).”
2- It is encouraged to jog slowly through the first three rounds around the Ka`bah. One should walk quickly, keeping close to the Ka`bah as much as possible, while taking short steps. During the next four rounds, one should walk at a normal pace. If one is unable to jog or get close to Ka`bah, because of the area being overcrowded, one may perform one’s tawaf in any way possible.
Touching the Yemeni corner (Ar-Ruknu Al-Yamani) is encouraged, and so is kissing or touching the Black Stone in each of the seven rounds of Tawaf, if possible.
3- Remembering Allah and supplicating to Him as much as possible is also encouraged. For this purpose, one may choose any supplications that one feels comfortable with, without restricting oneself to any particular supplications or repeating what others may be saying.
There are no set supplications prescribed for this purpose. The supplications that some people consider to be prescribed for various rounds of tawaf are not authentic. There are no such supplications reported from the Prophet (peace and blessings be upon him). One should pray for oneself, for one’s family and for the Muslims for anything that is good in this life or in the hereafter.
Allah Almighty knows best.