Simply follow the directions on the State Department's website:

https://travel.state.gov/content/tra...st-stolen.html

1. Yes, you may report online.
2. Yes, you will need to apply for a replacement passport. You may complete the forms online, print them and take them to a Passport Acceptance Facility (typically a Post Office or the like), along with the required documents such as photos, and payment.

There are options should you have immediate travel, but those do not apply here.

Do note that reporting the passport is critical. A valid US passport is worth thousands of dollars on the black market and if it falls into the wrong hands and is not reported stolen, can cause you ongoing, time-consuming and expensive grief.