This is how you wish a happy holiday. You say поздравляю вас (pazdravlyayu vas) then the holiday or occasion in the instrumental.
…с Новым Годом (with the New Year)
…c днем рождения (with your birthday)
I have spent the last several hours Skyping with my various Russian and Ukrainian friends “congratulating” them with the New Year.
I even taught my three year old to say “С Новым Годом” (s novym godom), which is a shortened way to wish happy New Year. It was an absolute crowd pleaser.
My American friend and I were laughing about how awkward it sounds in English to ‘congratulate’ someone on Christmas or some other holiday, like you had something to do with its existence and thus deserve praise.
For a language that loves passivity and a culture that loves modesty they sure love to take the credit when it comes to holidays.
So congratulations to everyone for making New Years happen. Good work!