TAWAAF OR CIRCUMAMBULATION
Lexically, Tawaaf means to turn, walk, etc around something. Islamically, Tawaaf is the circumambulation of the kaba seven times in anti-clock wise direction. People usually do this during Umrah or Hajj. It is the second compulsory act of Umrah. If one omits this act whether knowingly or because of ignorance of the rule, the Umrah becomes null and void, and as a result one's Ihram also becomes void. A Tawaaf is a complete act of going round the Kaba seven successive times.  
The Muslim who affirms the Oneness of Allah obeys the command of Allah in all matters, great and small. When he hears the words of Allah (interpretation of the meaning), “and circumambulate the Ancient House (the Kaba at Makkah)”Qur’an.Surah Hajj 22:29, he cannot help but obey them, so he circumambulates the sacred House out of love for Allah and in obedience to Him, hoping for mercy from Allah and fearing His punishment. And he does not go beyond what he has been commanded to do of Tawaaf, so he does not touch the stones of this House or think that it can bring benefit or cause harm.
Tawaaf is started from Hajreh Aswad (stone) corner. Rukn-e-Yemeni (stone in direction of Yemen ) is in one corner and next to Rukne Yemeni is the Hajreh Aswad stone corner. From Rukn-e-Yemeni you have to recite dua " Rabbana Aatina Fid-Duniya Hasanathaw Wa Fil Aakhirathi Hasanathaw wa Qeena Aza Ban Naar". This dua should be recited from rukne yemeni to hajreh aswad during every round of Tawaaf.
Also 2 rakaats Nafil Namaz near Muqam Ibrahim alaihis salaam.If you did not get the place for this particular salah at this place then at your convenient place in Masjid E Haram. (Fatwa by Shaik BinBaaz)
Except for the specific supplication between the last stretch of each ‘Tawaaf’ of the Kaba, ie. between ‘rukne Yamani’ and ‘Hajar Aswad’, there are no specific or particular duas recorded in the authentic Sunnah which one needs to recite during the ‘Tawaaf’. One may praise The Lord Most High and/or supplicate the Lord Most Merciful in any language and words in the ‘Tawaaf’. It is Sunnah to recite this supplication during the last stretch of each ‘Tawaaf’ between the ‘rukne Yamani’ and the ‘Hajar Aswad’:
‘Rabbana aatena fid-dunya hasanah, wa fil-aakherate hasanah, wa qina adaab-an-naar.’ Quran.Surah Baqrah 2:201
(O our Lord, give us the good in the world, and give us the good in the Hereafter, and save us from the torment of the Fire.)
There are many types of Tawaaf around the Kaba:
Tawaaf al-ifaadah during Hajj, which is also called Tawaaf al-ziyaarah (Tawaaf of visiting). It takes place after the standing in ‘Arafah, on the day of al-Adha or after it. It is one of the pillars or essential parts of the Hajj.
Tawaaf al-qudoom (Tawaaf of arrival) for Hajj. This is done by the pilgrim who has entered Ihram for Hajj and by the pilgrim who is doing Qiraan, i.e., joining ‘Umrah and Hajj, when he reaches the Kaba. It is one of the obligatory duties or Sunnahs of Hajj – there is a difference of scholarly opinion.
Tawaaf al-wadaa’ (the farewell Tawaaf), which is done after completing the actions of Hajj and when one has decided to leave Makkah al-Mukarramah. It is obligatory, according to the more correct of the two scholarly opinions, for all pilgrims except women who are menstruating or bleeding following childbirth, and the one who fails to do it must sacrifice an animal of the type that is valid as an udhiyah.
The Tawaaf of ‘Umrah. It is one of the pillars or essential parts of ‘Umrah, which is not valid without it.
Tawaaf in fulfilment of a vow made by one who vowed to circumambulate the Kaba. It is obligatory because of the vow.
Each of these Tawaafs must include seven circuits, after which the person offers two rak’ahs behind Maqaam Ibraaheem, if possible; if he cannot do that then he may offer the prayer in any other part of the mosque. 
A woman who is in menses when she wears or is already wearing Ihram of Umrah has to wait until her period ends to perform Ghusl and fulfill her obligations if there is enough time for her to complete the Umrah.
If the period continues until the time of wearing the Ihram of Hajj-e-Tamattu, there are two options open to her:
If the pilgrim does Tawaaf al-Ifaadah and forgets one of the circuits, and a long time has passed, then he should repeat his Tawaaf, but if only a short time has passed, he should make up the circuit that he missed.
Tawaaf for ‘Umrah or Hajj must be seven circuits, and it is not acceptable to do less than that, because Allah has enjoined Tawaaf and said: “and circumambulate the Ancient House (the Kaba at Makkah)” Qur’an.Surah Hajj 22:29
And the Prophet (May Allah honour Him and grant Him Peace) explained that by his actions, and he did seven circuits and said: “Learn from me your rituals of Hajj.” Sahih Al Muslim 2286
Al-Nawawi (May Allah have mercy on him) said: The condition of Tawaaf is that it must be seven circuits, each one starting and ending at the Black Stone. If one step of the seven is omitted, then his Tawaaf does not count, whether he stays in Makkah or has departed and returned to his homeland, and it cannot be rectified by offering a sacrifice or anything else, from al-Majmoo’ (8/21). 
Muwalaat: All the seven rounds should be completed one after the other without stopping.
Shaykh Muhammad ibn ‘Uthaymeen (May Allah have mercy on him) said: “It was proven in al-Saheehayn that Ibn ‘Abbaas (R) said: “The people were commanded that the last thing they should do in Makkah was to circumambulate the Ka’bah, but an exception was made for menstruating women.” Sahih Al Bukhari, 1755; Sahih Al Muslim, 1328. So Tawaaf should be the last action of Hajj that a person does. 
People make several mistakes when performing the farewell Tawaaf:
Everything in the universe, from the tiny atoms to huge galaxies, is in a state of Tawaaf. In the atom, electrons turn around the nucleus, which is like the heart, with a dizzying speed; in the galaxy, billions of stars rotate around the center of the galaxy with an incredible speed. They rotate as if they worship the Creator that created them.
As it is stated in the Qur’an, each swims along in an orbit, Qur’an.Surah Yaseen 36:40, Allah created such system. Similarly Allah gave command to Muslims for Tawaaf. We are not innovating anything new in this circumambulation. .
This is an evident lie. If any Muslim wants to offer Salah, So someone may offer in North or South or East or West direction. Now question comes that which direction should he face. So Allah commands us Muslims to face Kaba as it is mentioned in Qur’an: “We see the turning of thy face (for guidance) to the heavens: now shall We turn thee to a Qiblah that shall please thee. Turn then thy face in the direction of the Sacred Mosque: wherever ye are, turn your faces in that direction.” Qur’an. Surah Baqarah 2:144
Kaba is the Qiblah i.e. the direction Muslims face during their Salah (Prayers). It is important to note that though Muslims face the Kaba during prayers, they do not worship the Kaba. Muslims worship and bow to none but Allah.
1. Islam believes in firm unity
If some Muslims live towards the west of the Kaba they face the east. Similarly if they live towards the east of the Kaba they face the west. Hence following unity among Muslim Ummah.
2. Hadith of Umar (R)
Regarding the black stone, hajr-e-aswad, there is a hadith (tradition), attributed to the illustrious companion of the Prophet Muhammad (May Allah honour Him and grant Him Peace), Umar (R) narrates “I know that you are a stone and can neither benefit nor harm. Had I not seen the Prophet (pbuh) touching (and kissing) you, I would never have touched (and kissed) you”. Sahih Al Bukhari Vol 2: 675, 1597 (NE) and Sahih Al Muslim 1270
3. People stood on Kaba and gave the adhan
At the time of the Prophet, people even stood on the Kaba and gave the ‘adhan’ or the call to prayer. One may ask those who allege that Muslims worship the Kaba; which idol worshipper stands on the idol he worships?
So there is a great and clear difference between the actions of those who believe in Tawheed and Islam, and the manifestations of idolatry and shirk. The one who does not pay attention to this difference will become confused, and will no longer be able to differentiate between kufr and faith.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
As for submission, devotion of the heart and acknowledgement of divinity and Lordship, these can only be directed towards Allah alone, and if directed towards anyone or anything else they are utterly false. As for prostration it is connected to the commands of Allah, because Allah has commanded us to prostrate to Him, and if He had commanded us to prostrate to any of His creation other than Him, we would have prostrated to that one in obedience to Allah if He wanted us to venerate the one to whom we were prostrating. As He has not commanded us to prostrate, then we should not do it at all. The prostration of the angels to Adam was an act of worship to Allah, obedience to Him and a means of drawing closer to Him, and it was a way of honouring and respecting Adam. And the prostration of Yoosuf’s brothers to him was a greeting, Majmoo’ al-Fataawa (4/360, 361).
Thus we may differentiate between many cases in which actions may appear outwardly to be similar, but in fact one is Islam, Tawheed and faith, whereas the other is shirk, kufr and idolatry. This clarifies that Kaba is a sacred structure in Islam and Muslims do not worship it.