The word जन्मदिन means “birthday”. This word is sometimes hyphenated as जन्म-दिन. It is a literal compound of जन्म (“birth”) and दिन (“day”).
Here are some sentences related to birthdays:
आज मेरा जन्मदिन है – “Today is my birthday”
आपका जन्मदिन कब है – “When is your birthday?”
(आपके) जन्मदिन की शुभ कामनाएं – “Happy birthday” (शुभ = “good”, कामनाएं = “wishes”)
Sometimes, शुभ कामनाएं is written as one word: शुभकामनाएं.
Sometimes the word हार्दिक (“hearty”, “heartfelt”) is added:
जन्मदिन की हार्दिक शुभकामनाएं
जन्मदिन मुबारक हो – “Happy birthday”, literally “may your birthday be blessed/auspicious/fortunate”
Sometimes this phrase is abbreviated as जन्मदिन मुबारक.
अपना जन्मदिन कैसे मनाएंगे – “How are you going to celebrate your birthday?”
The verb मनाना can be used to mean “celebrate”.