Formal:
* Пожалуйста (Pozhaluysta) - This is the most common and neutral way to say "please." It's appropriate in most situations.
Informal:
* Пожалуйста (Pozhaluysta) - This is also used informally.
* Будьте добры (Bud'te dobry) - Literally "be kind," this is more polite than "Pozhaluysta" and emphasizes the favor being asked.
* Не могли бы вы... (Ne mogli by vy...) - "Could you..." This is a very polite and formal way to ask for something.
* Можете, пожалуйста... (Mozhete, pozhaluysta...) - "Can you, please..." This is a polite way to ask for something, but less formal than "Ne mogli by vy..."
Example:
* "Could you pass me the salt, please?"
* Formal: Не могли бы вы передать мне соль, пожалуйста? (Ne mogli by vy peredat' mne sol', pozhaluysta?)
* Informal: Передай мне соль, пожалуйста. (Pereday mne sol', pozhaluysta.)
The choice of which phrase to use depends on the situation and your relationship with the person you're talking to.