No need ot pre-book. Just be aware, that from the international terminal there is only one bus per hour. From the other two terminals there is a bus departing every 15 minutes. We had just missed the one bus and decided to take an internal shuttle bus to Terminal 2. So, I can only tell you about the procedure from there, but I would think it is very much the same at the international terminal.
We arrived at one bus stop and saw that there were several stops for the Airport Limousine just a little further down, so walked there. Asked for the one to Disney and were directed to the appropriate one (I think it was #4, but you can check that on the website of the Airport Limousines).
There we were informed that we had to get a ticket from the machine. There were several ticket machines available in the wall of the terminal next to the bus stops. The machines could be switched over to English (like all the ticket machines for trains and subways that we encountered) and it was very self explanatory how to get the ticket. You have to choose your departure time, of course we chose the closest one, just 5 minutes later. We even had one of the Airport Limousine workers help us with the ticket purchase. People (like all over Japan) were very friendly and helpful. With the tickets we went back to the bus stop where we were told which of the three lines marked on the ground was ours, we lined up, they took our luggage and tagged it and gave us the receipts (keep them, they do check when you get off the bus that you are receiving your correct luggage). When the bus pulled up, we got on it, the luggage was loaded, the doors closed and the Airport Limousine personel bowed to say goodbye to the departing bus.
There are announcements in Japanese and English as to which stop is next and that you are supposed to press a button if you want to get off. We were the last people on the bus, so ours was the final stop anyway and for us there was no button pressing required.
It was so easy and convenient! I would definitely choose the Airport Limousine again in the future.