When you're a job seeker, it's easy to view every interview as if it's a high stakes event. You want to get the offer, even if it might not be the right job for you. It's easy to focus more on persuading the hiring manager than evaluating whether the position (and the company) are the right fit for you and your career. It's better to keep an open mind, do your research, ask questions and be open to the experience, rather than purely focusing on convincing the interviewer that you are the right choice.
That said, you may already be convinced that this is definitely the job you want. How do you persuade a hiring manager to give you the job? The very best way to persuade someone to take action is to put aside empty words, and show your results. Talk about what you have achieved in factual terms. Did you improve a process, and save your employer $500K? If that helps you be successful in the position you are interviewing for, then share that, instead of "I have experience redesigning processes for efficiency."
Ask perceptive questions that show insight into the organization and its needs. Find out what problems the hiring manager is having, and offer solutions that work. Approach the conversation as if you are consulting, and show the other person that you can resolve issues, remove barriers, and generate success.
Relate your experience to actual accomplishments that are relevant to what the hiring manager needs. Be confident, but not arrogant, in your communication style. Listen as well as talking, and ask great questions that demonstrate your understanding of the organization, its current needs, and the challenges the hiring manager is facing.
Above all, persuasion is based in trust, authenticity and transparency. Don't pretend to be someone you're not, and never inflate your qualifications in an effort to get the offer or misrepresent what successes you've had in the past. Don't pretend to understand the industry if you don't, or if you haven't done your homework on the business. Put your best foot forward, and whether you get the offer or not, you will make a positive impact on that hiring manager. You never know where that connection will lead!