The Korean symbol for the English word 'family' is 가족, or 'gajog'. This is also the symbol for the the word 'families'. The Korean for 'my family' is 내 가족, or 'nae gajog'.
Some other useful Korean word symbols connected with family:
mother - 어머니
father - 아버지
son - 아들
daughter - 딸
brother - 동생
Korean Sayings about Families
콩 심은데 콩나고, 팥 심은데 팥난다 - "children observe their parents and follow their example."
가는 말이 고와야 오는 말이 곱다 - "all friendships come second to family."
먼 친척보다 가까운 이웃이 낫다 - "a close neighbor is better than a distant relative."
YouTube offers a lot of help to anyone wanting to learn a new language, and this film shows you how to pronounce Korean family expressions: