The Tawaf of the Ka'bah is a depiction of the Tawaf that runs above the Jannat al Firdaws in the seventh heaven where the Arsh (Allah's throne) is situated. Angels do Tawaf continuously around the Arsh. The Tawaf of the Kaabah should make it easy for humans to understand the reality of Tawaf around the Arsh.
The circle begins from the Black Stone on the corner of the Ka-bah. If possible, muslims are to kiss or touch it, but this is often not possible because of the large crowds, so it is acceptable for them to simply point at the Stone on each circuit. They are also to make the Takbeer prayer (Allahu Akbar) each time they approach.
For men, it is recommended to make the first three circuits at a hurried pace, followed by four times, more closely, at a leisurely pace.
At the end of the circling, Muslims go to the Station of Ibrahim to pray two rak'ahs, and then try if possible to drink water from the sacred Well of Zamzam, before proceeding to the next ritual of the Hajj, the Sa'y.
Muslims are generally advised to "Make Tawaf" at least twice -- once as part of the Hajj, and again as their final activity before leaving Mecca.
There are several types of tawaf that can be performed:
Tawaf al-nisa is a second tawaf that is performed during Umrah & Hajj. This type of tawaf is only recognised by Shia scholars.
Tawaf Qudoom (The 'Welcome tawaf') is the tawaf performed by those not residing in Mecca once reaching the Holy city.
Tawaf Umrah refers to the tawaf performed specifically for Umrah.
Tawaf Widaa (The 'Farewell tawaf') is the tawaf performed before leaving Mecca.
Tawaf Ziyaarah/Ifadah (Tawaf al-Hajj)