You apply for US passport by filling form and paying fees. This happens after oath, when you are a US citizen, not just after interview. If you only had interview and not oath, you're not a US citizen yet and cannot apply for passport.
There's routine service, expedited and urgent.
The times for routine and expedited service can be found here (usually few weeks):
https://travel.state.gov/content/travel/en/passports/how-apply/processing-times.html?os=io.....no_journeystrue&ref=app
Urgent is typically done within a day.