Same procedure as Celebrity. You get off the ship, get cleared by Customs and get back on the ship. However, there may be two differences. First, it appears that HAL recognizes your entire journey when you check in initially. If you stay in the same cabin, your room key will probably be good for the entire voyage. The dates on your card should reflect the entire journey. Second it appears that your onboard account may be connected through the entire voyage. OBC appears to be good on either leg and you get one bill at the end.
If you are talking about the combined voyages, one thing that irritates me is that HAL appears to have a more limited selection of cabins for those combined voyages. For example for a cruise I just booked on the Rotterdam, I could only book a couple connecting cabins for the combined voyage even though there were plenty of cabins open for both legs. HAL's representatives refused to budge and would only permit me to book those cabins. If wanted other cabins, I would have to book the two legs independently at a slightly higher cost. When I booked another cruise onboard, I didn't have this problem. At least that was my experience.