When you have children, you are a parent.

If you are a male parent, you are a father.

If you are female parent, you are a mother.

If one of your children is a boy, he is your son.

If one of your children is a girl, she is your daughter.

When a couple gets married, the man is the husband, and the woman is his wife.

A brother and sister both have the same parents.

One collective word to describe brothers and sisters is siblings. However this word is normally only used in written English, not orally.

Different Generations

Relatives and Extended Family

grandparents: the parents of your parents
grandfather: the father of your father/mother
grandmother: the mother of your father/mother
grandchildren: the children of your children
grandson: the son of one of your children
granddaughter:the daughter of one of your children
great grandfather: the father of your grandfather/grandmother
great grandmother: the mother of your grandfather/grandmother

uncle: the brother (or brother-in-law) of your mother/father
aunt: the sister (or sister-in-law)of your mother/father
cousin: the child of your aunt/uncle
nephew: the male child of your brother/sister
niece: the female child of your brother/sister

The In-Laws

The in-laws are the members of the family of your spouse (the person you are married to) or via a marriage in your family:

father-in-law: the father of your spouse
mother-in-law: the mother of your spouse
son-in-law: the husband of your daughter
daughter-in-law: the wife of your son
brother-in-law: the husband of your sister
sister-in-law: the wife of your brother

Note: To refer to more than one brother-in-law or sister-in-law etc. we has an S to the brother/sister part.
e.g. My brothers-in-law are fun. My sisters-in-laws are crazy.

The Family Mix

Nowadays in many countries a person can get married more than once. These are the terms used to describe the "new" members of the family when someone gets remarried.

"Step-" means that you are related as a result of one parent marrying again

stepfather: the (new) husband of your mother but not your biological father
stepmother: the (new) wife of your father but not your biological mother
stepson: the son of your (new) husband / wife (he is not your biological son)
stepdaughter: the daughter of your (new) husband / wife (she is not your biological daughter)
stepsister: the daughter of your stepmother or stepfather
stepbrother: the son of your stepmother or stepfather

Sometimes one of your parents gets married again and they have more children. There

half-brother: the brother you have only one parent in common with .
half-sister: the sister you only have one parent in common with.

Even if your parent didn't get married (and had the child outside of marriage), they are still your half-brother or half-sister.

However, note that it is common to still call your half-brother or half-sister just your brother or sister (without adding the half- part).

Check out this chart comparing the relationships between different members of the family: