The four magic words are: “I want the job.”
If you’ve done all your research on the company and you like the person interviewing you and you know you want to work there, then you have to speak up and say so. Don’t end the interview by saying, “I think this would be a great place to work. Thanks for the wonderful interview.” That’s too weak. You have come right out and say, “Thank you for the interview. I want the job. What are the next steps?”
As you do so, leave the door open so you can follow up with them rather than them having to follow up with you. You could say, “I’ll follow up with you in a week.” Chances are that because they’re interviewing many people and are overwhelmed, they’ll tell you not to follow up – that they’ll take care of it. But follow up anyway. You’ll never know what’s happening on a job’s status unless you follow up with the person.