2 questions: There is an open Product Owner position in company because previous product owner has left this company

I'd start with talking to and shadowing the people. Spend time with operations, customers, the development team, etc. Find out where they think the opportunities are and begin to formulate the vision from there. 

There will be people who have spent time and are invested in their product, prove to them you are to despite being new. 

I agree with Tony. Go in, ask a ton of questions and then ask more questions. I would suggest you taking these 3 questions and asking your leadership because you need an idea of their expectations for your role. Overall, there really are no defined steps to follow in this situation. It is like with any new job you get, it takes time to get acclimated and you'll have to find what works the best. Just remember, you're not going to know everything you need to know in a week or even a month. It takes time, so lean on your teams to help you.

Perhaps there are no steps to follow at all. In Scrum, you should expect things to be emergent, and to inspect and adapt the things you do and how you do them.

Nevertheless, I would suggest you might start by learning what product value is, and how to best communicate it.