"Io ti leggo un libro."
Just remember that "ti" means "to you" in this situation. You could even go as far as to think of it as a contraction of "a+tu". Same with "mi" ("a+io"), "lo/la" ("a+lui/a+lei"), "ci"("a+noi"), "vi"("a+voi"), but "li" I'm a little confused about, actually. I'm not sure it's used the same way... Maybe you just say "a loro" for this type of sentence? You know, maybe you should disregard everything I said, because I hardly know what I'm talking about. Maybe someone more knowledgeable can reply.
Always follow the subject and verb conjugation. Io Leggo -- I read Because this is first person singular, the action is being performed by "I", not to or for "I". The direct and indirect object pronouns (mi, ti, etc) always indicate who or, or to whom or to what, the action is directed.