Based on the level of respect or formality, you can say "This is my sister" in Korean in 3 ways:

Man's elder sister

• Informal: nae nuna-ya (내 누나야)
• Formal: jae nuna-yeyo (제 누나예요), jae nuna-ipnida (제 누나입니다)
• Very Formal: jeo-eui nunim-isipnida (저의 누님이십니다)

Lady's elder sister

• Informal: nae eonni-ya (내 언니야)
• Formal: jae eonni-yeyo (제 언니예요), jae eonni-ipnida (제 언니입니다)
• Very Formal: jeo-eui eonni-isipnida (제 언니이십니다)

Man's and Lady's younger sister

• Informal: nae dongsaeng-iya (내 동생이야)
• Formal: jae dongsaeng-iyeyo (내 동생이예요), jae dongsaeng-ipnida (제 동생입니다)
• Very Formal: jeo-eui dongsaeng-ipnida (저의 동생입니다)

- this is (introducing someone): ida (이다)
- my: na-eui (나듸), jeo-eui (저의), nae (내), je (제)
- man's elder sister : nuna (누나), nunim (누님)
- lady's elder sister : eonni (언니)
- younger brother: dongsaeng (동생)

Please refer to How to pronounce Korean Alphabet for the English pronunciation in this answer.