You have a great degree of flexibility in performing this ritual. The gods may be pleased in any order you choose; you may wish to do Thoth last, if possible, since you can not unlearn a skill/technology. Also, except for the opening and closing ceremonies, you and your partner may switch roles for each of the gods. All that matters is that one person perform the action, and the other speak the words. The prayer must come after the action. (it looks like the time is very non-critical - minutes later seems to work)
When reciting the words, they must be said in the Main channel; your spelling must be correct, but punctuation and capitalization do not matter. You may talk to each other with /tell, /chat, or in guild channels for coordination without affecting the ritual. Turns out you can speak normally in Main too, killing that myth ;)
The ritual does not consume the items used in the opening and closing ceremonies, or the milk, so you may borrow the milk and small diamond from someone else.
Upon completing the opening ceremony, a window will appear noting the your current standing with each of the six gods. When you successfully please a god, you will get a pop-up message, and your standing will be updated.
Finally, the entire ritual must be completed within 25 minutes, starting from when you complete the opening ceremony. You may not use navigation (waypoints) during the ritual.
Be sure to plan out where you will perform the initiation; the big factors in deciding a location are proximity to a school/university, water, deep desert, a patch of grass (for flax), and, of course, an altar. You can build a mine if one is not nearby, and you must build a ritual torch (or have someone build it for you), since ritual torches can only be used once. A ritual torch requires Ritual Item Construction 1 (tuition is 3 candles), and needs 1 board and 1 canvas to build.
This information was taken from http://egenesis.centralserver.net/man-rituals.html
(Now that pasting into the game works, this may be handy)
Praise Horus, King of Egypt
Praise Isis, whose seed is forever fertile
Praise Osiris, who was Reborn like the Scarab
Praise Ra, of the Blazing Eye
Praise Thoth, the Magician who created Science
Praise Bastet, who teaches grace and elegance
(See also Tests)