Well you cannot book online. But you really donot need to book as ganga aarti is conducted on ganga river ghat which are huge and spacious. Best way to watch it is to go a bit early and sit there. Or go to opposite side and sit there. Ganga aarti is all about the atmosphere there and you can enjoy it by sitting there.
You can be seated by 4 - 4:30 PM in the first row as it gets fully packed at the time of Arti.. there is no need of any prior booking. However, you might want to contribute by paying in cash to the authorized people who would be present there during the arti... People usually occupy the first row adjacent to the Ganga river.
No need to book anything you can visit directly.
Get quick answers from Ganga Aarti at Haridwar staff and past visitors.