Ground transport and overnight stay

With a handful of exceptions, airlines do not generally provide ground transfers between airports or overnight accommodations. Those are usually costs you incur by purchasing a connection like this. I find no indication Hawaiian Airlines offers any such service in Japan.

As such, you'll need to pass through immigration and enter Japan (which could require a visa depending on your nationality, which you haven't specified), collect any checked luggage, travel to Narita, and check in for your next flight.

The Haneda Airport website recommends either a series of train connections or a shuttle service (you can see our previous question on this topic). However, the limousine bus service stops running too early for your purposes, and Narita is difficult to reach by train late at night. dda's suggestion of staying somewhere in Tokyo where you can catch an early morning direct train to Narita after you rest is a good one. You could also stay near Haneda, but will have a longer trip in the morning.

Hotel reservations are your responsibility, and you can book them at the hotel of your choice using any number of online hotel booking websites to compare options.

The airline(s) sold you plane tickets. The rest is up to you. Since you arrive quite late in Haneda, I would recommend booking a hotel in Shinagawa (like one of the Prince Hotels), and the next morning take an early Narita Express train to Narita.

There's a 06:05 Narita Express that puts you in Narita at 07:15. Plenty of time for your 09:30 flight.

An important point, mentionned by Zach Lipton, is the visa. I assumed you were from the US (and thus wouldn't need one), but I should've covered all bases indeed.