Tawaf is the circling of the Kaaba in Mecca seven times. The following illustration depicts the proper order and circumambulation of the Tawaf:
Rushing quickly with short steps: This is a Sunnah that applies only to men and only in the first three circumambulations. This counts for the arrival Tawaf of Hajj (Tawaf Al-Qudum). Also with the Tawaf of 'Umrah (i.e. not in the Tawaf Al-Ifada, or a voluntary Tawaf).
Exposure of the right shoulder: This is a Sunnah that applies only to men (like hastening). It is performed only during the arrival Tawaf of Hajj or the Tawaf of 'Umrah. Upon completion of the tawaf, the shoulder is immediately covered again.
Touching the black stone with the right hand and kissing the stone at the beginning of the tawaf. Doing this during the tawaf when passing it. As well as at the end of the tawaf when possible. If this is difficult due to the crowd, one merely touches the black stone with the right hand and kisses it. If this is also difficult, the right hand is raised briefly with the palm towards the black stone as if in greeting. And the takbiir is said without kissing the hand afterwards. It is Sunnah to touch the black stone again with the right hand without kissing the stone. Also possible when one has prayed the two sections of prayer after the Tawaf and goes to the Sa'ii.
Note: It is not permitted to go into the jostling crowd in front of the black stone so as not to crowd anyone and not to harm an yone. Avoiding direct contact with the Black Stone is then a duty that takes precedence over the Sunnah of kissing or direct contact. It is specifically the duty of women to avoid any crowds and jostling as much as possible. This is in order to protect their 'Aurah (read: their bodies) from being looked at and touched by strange, non-mahram men.
Saying the following words with the beginning of the Tawaf:
Supplication
❁ بِسمِ اللَّهِ، واللَّهُ أكْبَرُ، اللَّهُمَّ إيمَاناً بِكَ وَتَصدِيقاً بِكِتابِكَ، وَوَفاءً بِعَهْدِكَ وَاتِّباعاً لِسُنَّةِ نَبِيِّكَ صلى اللّه عليه وسلم ❁
❁ Bismillah, wa-llahu akbar, Allahumma iimaanan bika wa tasdiiqan bikitaabika wa wafaaan bi'ahdika wa-tibaa'an lisunnati nabiyika Muhammadin –Salla-Allahu 'alaihi wa sallam ❁
❁ In the name of Allah and Allah is greatest, O Allah, believing in You and confirming Your Book and fulfilling the covenant with You and following the Sunnah of Your Prophet Muhammad -honor and salvation be upon him. ❁
Saying general supplications during the Tawaf. Also saying the following supplication between the Yemeni Corner and the Black Stone:
Supplication
❁ رَبَّنَا آتِنَا فِي الدُّنْيَا حَسَنَةً وَفِي الْآخِرَةِ حَسَنَةً وَقِنَا عَذَابَ النَّارِ البقرة: ٢٠١ ❁
❁ Rabbana aatina fid-dunya hassanah, wa fi-l akhirati hasanah, wa qinaa 'adhab an-naar ❁
❁ Our Lord, grant us good in this world and good in the Hereafter, and save us from the punishment of the (Hell)Fire. (Quran 2:201)❁
Touching the Yemeni corner with the right hand if it can be done without difficulty and jostling.
Praying the two Raka'ah behind the Maqam Ibrahim: The Maqam Ibrahim is on the side of the door of the Kaba. The two Raka'ah should only be prayed directly behind it if it does not affect anyone. Otherwise, these two Raka'ah can be prayed anywhere in the mosque. It is Sunnah to read Surah Al Kafirun in the first Raka'ah after Fatihah and Surah Al-Ikhlas in the second Raka'ah after Fatihah.