As it seems, if you are not with a group of 10 or more people, no advance booking can be made. http://www.hozugawakudari.jp/ryoukin.html
According to this page, departures (March 10 to Nov. 30) are at:
9:00, 10:00, 11:00, 12:00, 13:00, 14:00, and 15:30, but on weekends the boat leaves on somewhat irregular schedule - probably as they get full they might just leave. You just queue up and board. If you have tight planning for the rest of the day, I would probably show up a bit earlier than just 15 minutes prior to departure, but maybe that is ok as well.
Note that they say on Feb. 25 (already past, though) and Sept. 9, 2009, they will be closed for maintenance.