I haven't setup one myself but have been in one.
Some of the challenges and tasks are highlighted below.
1) Stakeholder engagement for necessary progress
2) Make sure you have adequate funding and acceptance from senior management. My company management believed in the PMO concept and we were never short of funds or support.
3) Setting up roles and laying out resources to manage the PMO. Think of it as definition and clarity before control.
4) How can you rollout changes ( trust me this can take years ).
1) Gather gather and gather as much information as you can.( Also need to find a way to store them, some kind of document retrieval system). My company invested in sharepoint. You will need some inputs, suggestions from your management and colleagues and adopt the the best suited for your ORG.
2) Converting Lessons learned to Best practices.
3) If your ORG is into multiple domains then a common adoption of best practices.