Explicación sobre los posesivos

possessive adjectives

my - mi(s)
your (fam.) - tu(s)
her - su(s) or de ella
his - su(s) or de él
your (pol) - su(s) or de ud.

our - nuestra (o, as, os) or de nosotros
your (fam pl) - vuestra (o, as, os) or de vosotros
their - su(s) or de ellas
their - su(s) or de ellos
your (pol pl) - su(s) or de ustedes

possessive pronouns

mine - mía (o, as, os)
yours (fam.) - tuya (o, as, os)
hers - suya (o, as, os) or de ella
his - suya (o, as, os) or de él
yours - (pol) - suya (o, as, os) or de ud.

ours nuestra (o, as, os) - de nosotros
yours (fam pl) vuestra (o, as, os) - de vosotros
theirs - suya (o, as, os) or de ellas
theirs - suya (o, as, os) or de ellos
yours (pol pl) - suya (o, as, os) or de ustedes

A definite article is needed before the pronoun, except if a form of the verb ser is used. The article is needed with ser to distinguish between two or more owners of different objects or for emphasis.

Ejemplos:

Ése es mi libro. Ése es mío. Ése es el mío.
That one is my book. That one is mine. That one (among others) is mine.
(as opposed to someone else's)

Ése es mi libro, aquél es de Sonia. El tuyo está en casa.
That one is my book, that one over there is Sonia's. Yours is at home.

Ése es mío, aquél es suyo.
That one is mine, that one over there is hers. (Making a statement of fact.)

Ése es el mío, aquél es el suyo.
That one is mine, that one over there is hers. (Distinguishing between the two owners.)

Note: Spanish does not use possessive adjectives when the owner is identified and if what s/he owns is part of her or his body. Instead a definite article is used.

Her molars hurt.  

Her molars are full of cavities.
A ella le duelen las muelas.
vs.
Sus muelas están llenas de caries.
 
.
.
I am going to wash my hands.
.
My hands are dirty.
Me voy a lavar las manos.
vs.
Mis manos están sucias.