We just returned from our 6 days on the Carnival Breeze this past Saturday. While this wasn't our first cruise, it was our first with our 19 month old son. Before we left, I scoured CC for any advice/help/tips for traveling with a toddler, so here is my $.02
1. Bring more diapers than you think you will need. You will probably need them.
2. They only serve apple juice in the mornings for free (on Carnival at least). We stocked our mini fridge in the room every morning with enough for the day.
3. Grab the little boxes of cereal at the breakfast buffet. They make for a great snack at the ports.
4. Find an empty lounge or conference area during the day and let your little one RUN. My son was in his stroller so much he needed to let off some steam.
5. Camp Carnival is for 2 and older, but on sea days they have a few hours where under 2 can play as long as a parent stays. My son loved playing with the toys and other kids!
6. You won't make it through an entire dinner in the MDR. If you do, please order a second chocolate melting cake for me
7. If you have a tablet or Kindle, bring it. My son watched movies and played Angry Birds in order to wind down at dinner or before bed.
8. We have a very strict schedule at home. Day 1 that was thrown out the window. Go with the flow, enjoy yourself, and try not to get caught up with scheduling.
9. ENJOY it. It's hard traveling with a kid, but it's worth it. Don't expect to do everything you want to do, but find things for everyone to enjoy. I didn't make it to every show, or get to play every game, but I got a totally different "mom" experience, which was cool