ITIL and COBIT

Answer:
There is no cookbook how to do it. COBIT is IT governance framework and ITIL is IT service management framework. You can see COBIT as interface between company (and its strategy, goals, risks...) and IT services. ITIL should enable excellence in management of your IT services (throughout their lifecycle) and COBIT should enable alignment of the IT organization with the goals of the business.
COBIT is much broader than ITIL and ITIL goes much more in details. Ideally, they are implemented together to integrate business and IT services.