We just returned from a great cruise to Bermuda on Royal's Anthem of the Seas. I had read a lot of reviews (and helpful tips) before we went and that REALLY helped. I hope to provide some tips for those traveling soon as well.
The first thing I would tell people is to ignore the "time" they chose to board the ship (and what is printed on your Set Sail Pass) and just get to Bayonne as early as possible!!! They will have you drive up with everyone else - funneling into two lanes which can be harrowing - and drop off your bags with a porter (who will expect a tip) and then you continue on to the parking garage which, for a 5 night cruise, is $100. This process took a while since the port was really crowded.
Then once you get into the terminal, they don't even look at your scheduled boarding time, they simply check you in on an iPad (if you've already done everything online at home which I HIGHLY suggest - you won't have to check-in at the big desks, just find someone with a turquoise shirt and an iPad) and have you sit in sections of blue and white chairs for the order in which you will board the ship. Those who are not lucky enough to sit in chairs stand around and then they "feed" those people into the chairs AFTER they start taking people from the chairs to board the ship. It's a little chaotic but everyone is in a good mood since you are all on vacation! A few more minutes boarding through the connecting hallways and then you are on!
A bit chaotic but fine.