Cat Ba is offshore from Hai Phong, and the standard route from Hanoi (roughly 4 hours total) is by combined bus and ferry. Several operators — Cat Ba Express, Hoang Long, Daiichi — run combined tickets that pick you up in Hanoi's Old Quarter, drop you on the ferry at Got harbour on Cat Hai island, cross the short sound by bus, and deposit you in Cat Ba Town. Booking online a day ahead is fine; turning up at the operator's Hanoi office in the morning also works.
The faster but pricier option is the speedboat from Tuan Chau (the Halong Bay tourist port), which takes 45 minutes — useful if you are already on the Halong side. The very brave can also ride a motorbike to Hai Phong and take the car ferry across. Note that the ferry suspends in stormy weather; build a buffer day into onward travel.