First phrases: essentials

Essentials:
Да - Yes
Нет - No

Спасибо! - Thank you
Пожалуйста! - Please (and You're Welcome)
Извините! - I am sorry  and Excuse me

The word Пожалуйста is used to mean "You're Welcome", after somebody says thank-you. Пожалуйста is pronounced a little different than it is written, you can basically forget the "уй".

Привет!  -  Hi  
Здравствуй (те)! - Hello!

Пока!  - Bye!(informal)
До свидания! - Good-bye!

Здравствуйте may be a little difficult for you to pronounce at first, but it is the most common Russian greeting so you should try to practice it. Привет is also commonly used with friends.

Я не понимаю. - I don't understand
Я не знаю. - I don't know