As we saw in the last lesson, there are three genders in Russian – masculine, feminine and neuter. Each of these can necessitate a different ending on the possessive pronoun.
The endings for мой are мой (masculine), моя (feminine) and моё (neuter).
твой declines in the same way as мой.
наш has these forms: наш (masculine), наша (feminine), and наше (neuter) - which are actually just the "soft" versions of the endings above.
ваш follows the same pattern as наш.
его, её and их, however, never change.
A complete table of the possessive pronouns (including the plural forms) is available.