The Prophet ﷺ said: take your rites from me. The main rites are ihram, being at Arafah on the 9th of Dhul-Hijjah, the tawaf of the Kaaba (tawaf al-ifadah) and the sa'i between Safa and Marwa. The Prophet ﷺ said: Hajj is Arafah.
1The order of the rites (Hajj Tamattu')
Ihram at the miqat with the intention for Umrah, then tawaf and sa'i for Umrah, and shorten or shave the hair, and exit ihram.
On the 8th, ihram again for Hajj and go to Mina.
The 9th: stand at Arafah from noon until sunset. This is the pillar of Hajj. Then go to Muzdalifah, pray Maghrib and Isha combined and spend the night there.
The 10th (Eid): stone Jamrat al-Aqabah, sacrifice, shave or shorten the hair, then tawaf al-ifadah and sa'i.
The 11th to 13th: stay in Mina and stone the three jamarat after noon each day. Leave after the 12th if in a hurry, or stay until the 13th.
The farewell tawaf before leaving Makkah.
2The pillars and the obligations
The pillars (without which Hajj is invalid): ihram, standing at Arafah, tawaf al-ifadah and the sa'i (in most schools).
Other obligations: ihram from the miqat, staying at Muzdalifah and Mina, stoning the jamarat, shaving or shortening, and the farewell tawaf. Missing one of these requires a sacrifice (dam).
Things forbidden in ihram include cutting the hair and nails, perfume, covering the head (men), sewn clothes (men), hunting, intercourse and marriage.
Where the schools differ
The four Sunni schools agree on the main ruling above and differ in these points. No school is preferred here.
The sa'i is a pillar of Hajj in the Shafi'i, Maliki and Hanbali schools (in the well-known view). In the Hanafi school it is an obligation (wajib), and missing it requires a sacrifice.
Three forms of Hajj. Tamattu' (Umrah first, then Hajj), Qiran (both together) and Ifrad (Hajj only). The Hanbali school prefers tamattu', the Hanafi school prefers qiran, and the Shafi'i and Maliki schools prefer ifrad.
Note
Hajj has many details. Learn them with a guide from your Hajj group, or from a trusted scholar, before you leave.
Hija ni miezi maalumu. Na anaye kusudia kufanya Hija katika miezi hiyo, basi asiseme maneno machafu wala asifanye vitendo vichafu wala asibishane katika Hija. Na kheri yoyote mnayo ifanya Mwenyezi Mungu anaijua. Na jitengezeeni zawadi. Na hakika bora ya zawadi ni uchamngu. Na nicheni Mimi, enyi wenye akili!
Si vibaya kwenu kuitafuta fadhila ya Mola wenu Mlezi. Na mtakapo miminika kutoka A'rafat mtajeni Mwenyezi Mungu penye Masha'ril Haram. Na mkumbukeni kama alivyo kuongoeni, ijapo kuwa zamani mlikuwa miongoni mwa walio potea.
This is general information, not a fatwa. For your own situation, ask a qualified scholar.
Fiqh questions
The rites of Hajj in outline
The Prophet ﷺ said: take your rites from me. The main rites are ihram, being at Arafah on the 9th of Dhul-Hijjah, the tawaf of the Kaaba (tawaf al-ifadah) and the sa'i between Safa and Marwa. The Prophet ﷺ said: Hajj is Arafah.
Is this a fatwa?
No. It is a summary of well-known rulings with their evidence. For your own case, ask a qualified scholar.
What if my school differs from this answer?
Follow the view of the school you follow and the scholar who teaches you. The page lists the differences of the four schools.