Once the "thank you" letter has been sent, your role in the job search is to work toward an offer. By staying in close contact (at least once a week) with your primary company contact, you will be continually aware of the process. And the contact will be continually aware of your interest.
Always make sure you know the next step in the process. How? By asking directly.
"I am very interested. What is the next step?"
If you are straightforward and direct, the contact will keep you posted as to your progress. If you are no longer under consideration, you will be informed. If there are further interviews pending or your background is being reviewed by others, you will be informed. If the company is getting ready to put together an offer, you will be informed. Stay close to your contact and be ready to act on a moment's notice.