"Product owners are key players in agile development projects. Often the most invested in the outcome a project, project owners direct development teams towards achieving key goals. Teams looking for product owners will be searching for candidates who have the ability to create a clear vision for the future of the product, prioritize objectives, and successfully lead a team to delivering results."
Imagine you are a newly minted product owner with no team. How would you execute on your product vision?
First establish the most important requirements and clarify them to a full extent. Start simple and work your way up on each iteration taking into account scope, constraints, dependencies, and schedule while keeping your eye on the big picture.