Tawaf is circling the Kaaba seven times, counterclockwise, beginning and ending at the corner containing the Black Stone, with the Kaaba kept on the pilgrim's left shoulder throughout. Each circuit is ideally accompanied by dhikr and personal supplication, though no specific wording is obligatory beyond a few du'as reported from the Prophet ﷺ. Men are encouraged to walk briskly (ramal) during the first three circuits of tawaf al-qudum (the arrival tawaf), then walk normally for the remaining four; this isn't repeated in tawaf al-ifadah.
Conditions scholars generally require include a valid intention, covering the awrah, and the tawaf taking place within the mosque boundary (which today extends beyond the original mataf area to accommodate crowds). Most scholars (Maliki, Shafi'i, Hanbali) hold that ritual purity (wudu) is a binding condition for a valid tawaf, treating it similarly to prayer; Hanafi scholars consider purity obligatory (wajib) but say tawaf performed without it is still valid, though a dam is owed. After tawaf, it is sunnah to pray two rak'ahs near Maqam Ibrahim if possible, or elsewhere in the mosque (Quran 22:29).