Which one should I use thy/thine
Thy and thine are archaic forms corresponding to your and yours respectively. Use thy where you would use your (but see note at end of answer) and thine where you would use yours.
Her and hers do not have alternate/archaic forms. Her is used as a possessive the same way my or your is, and hers is used like mine or yours.
(Note: if the noun placed after thy begins with a vowel sound, use thine instead: thy book, but thine eyes. Archaically, the same was done with my and mine, but this is no longer common usage outside of some poetic use.)