Once you are in the terminal go to the Norwegian desks and use the self-service machines to obtain your boarding pass. Any problems just go to the desk and speak to someone. Then head for the departure gates.
If you can check in online and print your boarding pass, then you will not have to check in at the airport and can go straight to security since you only have a carry-on bag. If you do not/cannot check in online, then you'll need to stop by the Norwegian counter to check in and get your boarding pass.
Be sure to follow the rules for liquids/gels and other restricted items in your carry-on. These can be found on www.tsa.gov. You will have to remove your shoes, belt, and coat before going through the body scanner. This process and these rules are all the same no matter what airline you are flying.
You should arrive 3 hours early since it is an international flight.
It is not really different than whenever you last flew, except there are now restrictions on liquids in your carry on bag if you last flew really a long time ago.
There is no passport control when exiting the USA. If you have only a carry on bag then you can print your boarding pass at home and go directly to Security.