A director should resign by written notice. That can be effective immediately. The company must register the notice of resignation at the Australian Securities and Investments Commission within fourteen days or it commits an offence [Corporations Act 2001 (Cth) s 205B]. This notice should be signed by the resigning director.
A director who resigns is still liable for any guarantee signed as a director (director's guarantee). These documents are enforceable as contracts and are still enforceable against guarantors who are no longer directors. It is only because they are usually signed by company directors that they are called 'director's guarantees'.
A director remains personally responsible for any liability under the Corporations Act 2001 (Cth) which was incurred by the company while that director was still acting as a director, see Criminal offences. However, that director is not responsible for any liabilities incurred after the resignation.