The First Tradition:
The Masquerade
Thou shall not reveal thy true nature to those not of the Blood. Doing such shall renounce thy claims of Blood.
The First Tradition is the most important of all, and one breaks this law at the risk of death. The Masquerade is a simple concept: simply keeping one's vampiric nature to themselves when around non-vampires. You do not speak of it. You do not use obvious supernatural abilities. You seek to remove evidence of supernatural activity when you find it, lest the mortals discover that the world isn't what they believe it to be.
The Second Tradition:
The Domain
Thy domain is thine own concern. All others owe thee respect while in it. None may challenge thy word while in thy domain.
The Second Tradition speaks of the concept of "my house, my rules." It largely benefits the single ruler of any given Camarilla city, who is referred to as a Prince regardless of the gender of that ruler. The Prince is to be treated with the greatest respect, since every vampire in his/her Domain is living on what is essentially the Prince's land.
The Third Tradition:
The Progeny
Thou shall only Sire another with the permission of thin Elder. If thou createst another without thine Elder's leave, both thou and thy Progeny shall be slain.
The Third Tradition stems in part from the Second. A vampire is not permitted to sire a childe in a Prince's Domain without the permission of that Prince. Doing so means death for both sire and childe if the crime is discovered.
The Fourth Tradition:
The Accounting
Those thou create are thine own children. Until thy Progeny shall be Released, thou shall command them in all things. Their sins are thine to endure.
The Fourth Tradition continues from the Third, dictating how new childer are seen by society. They are not considered to be their own person, but instead are under the direct supervision of their sires. Their mistakes are considered mistakes of their sire, so it is understandable that many sires keep their childe out of the public eye and on a close leash until such time as they prove they can handle themselves with necessary decorum. Once that time comes, a sire Releases their childe from the Accounting, and the childe is considered a true member of the Camarilla, albeit a mere neonate.
The Fifth Tradition:
Hospitality
Honor one another's domain. When thou comest to a foreign city, thou shall present thyself to the one who ruleth there. Without the word of acceptance, thou art nothing.
The Fifth Tradition is a simple one in concept. If a vampire is to visit another's Domain, they need to introduce themselves and seek permission to reside there, even briefly. It's only polite, after all.
The Sixth Tradition:
Destruction
Thou art forbidden to destroy another of thy kind. The right of destruction belongeth only to thine Elder. Only the Eldest among thee shall call the Blood Hunt.
The Sixth Tradition is appropriately the final one of the list, given that it pertains to the ending of a vampire's life. It is generally not permitted for a vampire to take the life of another, but all bets are off if the Prince has declared the life of a vampire in his/her Domain to be forfeit. All in a city are expected to answer the call of a Blood Hunt, though such hunts are an extreme measure reserved for truly despicable criminals.