I have mentioned the resources provided by the Project Management Institute and the Office of Government Commerce (now Axelos) but there are also some of my books that provide a more straight forward alternative:
If you want detailed guidelines for the implementation of all the things I’ve been talking about, they are all set out in Project Program and Portfolio Management in easy steps.
If you want guidelines for developing project management excellence, they are set out in Effective Project Management in easy steps.
If you are running agile project, then guidelines for developing agile project management excellence are set out in Agile Project Management in easy steps.
And last but not least if you are wondering where you will find the time to do it all then Effective Time Management in easy steps will provide you the answers.
So draw up a list of what you want to achieve and plan and manage the project like any other major business change. I say project but it could require a program (unless your organisation is already a good way up the capability maturity matrix) as it is likely to take several years to implement fully (and that by definition that should be a program not just a project).
Your mission, should you choose to accept it, is to produce a high-level plan for what you want to achieve, then sell the benefits of these best practices to your organisation. If you need any help I am always pleased to offer help or advice to fellow professionals and this is the URL of my web site should you wish to contact me: johncarroll.org.uk