Family words come in neat masculine/feminine pairs:

Masculine	Feminine	English
el padre	la madre	father / mother
el hermano	la hermana	brother / sister
el hijo	la hija	son / daughter
el abuelo	la abuela	grandfather / grandmother
el tío	la tía	uncle / aunt
el primo	la prima	cousin
el marido	la mujer	husband / wife

At home, padre and madre are usually papá and mamá. For wife, you'll often hear mi mujer in Spain; mi esposa sounds a little more formal.

To introduce someone, say este es for a man and esta es for a woman: Este es mi padre. Esta es mi abuela.