At Walt Disney World (and America in general) it's customary to tip for service-based roles. This extends to the Disney Cruise as well. Thankfully, Disney makes it super easy. You're automatically charged $13.50 per person, per night. This charge is added to your onboard account, which is then billed to your card towards the end of your cruise. This tip covers all your servers and your stateroom host. I know as Walt Disney World regulars, we often leave a couple of bucks on the hotel table when we're off to the parks, but there's no need to do that here, it's covered in part of your $13.50 per night.
On the final day of the cruise, you're given a sheet explaining how the gratuity is broken down, and who gets what. You don't have to do anything with this slip, you can just leave it in your room, it will still find its way to the right people. However, this does give you a chance to give your servers their gratuity slip (in the correct envelope) in person and a chance for you to personally say thank you when you see them for the final time for breakfast just before you debark. The stateroom host slip and envelope should be left in your room. You can give your stateroom host their envelope personally if you manage to see them roaming the halls in the morning. If you want to add more, you can do this at guest services or just slide some cash into the envelope with the slip. I put an extra $5 in each as a little extra thank you, but it's by no means required.
Each of the four sections are perforated and can be ripped off and placed in each of the provided envelopes. You can click the above image to open it in a new tab to zoom in.
You can go to Lumiere's or Rapunzel's for breakfast or lunch to have a table-service meal, but it's unlikely you'll get your usual evening servers (but if they see you, they will come and say hi!) You don't need to worry about gratuity here, as weird as it feels just getting up and leaving after you're finished eating. Think of it like you're paying the tips for your servers for all the work they do for you in the evening, but also what they do for others during breakfast and lunch, but somebody else is tipping the different servers who they get in the evening that you're getting for breakfast. (That was a mouthful, but I hope it's clear!)
If you buy a drink from any of the bars or lounges, an 18% gratuity charge is automatically added to the bill, which is added to your onboard account.
With room service, it is customary to tip $1 or $2 per plate. You can either give them cash, or they do have a slip with them you can sign to charge a few bucks to your onboard account.