I have been trying to memorize the words one at a time and it isn't sticking.
Usually, Korean people do not know well the pattern beyond 사촌(cousin)
We will focus to relation when I was a child.
Couple is 무(zero)촌. That is, there is no curtain. But parents and child has 일(one)촌. But we do not use 일촌. We use father (아빠, 아버지) or mother (엄마, 어머니). Similarly, grandfather(할아버지) or grandmother(할머니) has 이(two)촌.
Consider father's younger brother. me->father -> grandfather-> brother so that we call him 삼(three)촌 (uncle). But if he married, we use 작은아버지(small father) (And we call his wife 작은어머니)
Here we call his child 사(four)촌 (cousin). With respect to age, we use 사촌 동생, 사촌 누나 and so on.
Consider father's older brother : 큰(big)아버지.
Consider mother's brother : 외삼촌. (We call his wife 외숙모)
Consider father's sister and mother's sister : 고모 (aunt, her husband 고모부) and 이모 (her husband 이모부)
@Here 부 is China character implying man or husband.
Consider when we married or we are old :
(a) Older sister's husband is 매형 and conversely, he call me 처남. Younger sister's husband is 매제.
My wife call my older sister 시누이 and younger sister 아가씨. Conversely, my sister call my wife 올캐
(b) My younger brother's wife is 제수씨. Conversely, she call me 아주버님.
My wife call younger brother 도련님 (If he married, then it is 서방님). In further he call my wife 형수.
In further, consider wife's family :
Wife's older sister call me 제부 and her husband call me 동서. Wife's father and mother are 장인 어른 and 장모님.
Lastly, wife's older brother is 형님 (compare 처남)