Hi there,
The fastest way is to take a Narita Express from Narita Airport to Kawaguchiko. However, it is running only once a day on Saturdays and Sunday only (Leaves at 9:15 Arrives at 12:45). Then, you can take a local bus from Kawaguchiko to Mt. Fuji 5th station.
The other option is to take an airport limousine (https://www.limousinebus.co.jp/en/) from the airport to Shinjuku, and then take a highway bus from Shinjuku station to Kawaguchiko or Mt. Fuji 5th station.
You can book a ticket for the highway bus from the following website.
http://highway-buses.jp/fuji/
The timetable for Mt. Fuji 5th station is not listed on this website, however, if you click on Reservation button, you will see the whole timetable.
I hope this information helps.
Thank you