I did a lot of boat diving in FL not that long ago.
I had two bags, my mesh *wet* bag, and my reg bag which I treated as a dry bag. Have EVERYTHING you need to dive with maybe the exception of your computer/dive light in the wet bag. When you board throw the mess bag under the seat where your tanks are, and find a dry spot for your dry bag if it's NOT a true dry bag. This is generally in the cabin up front, or next to the front window on the lower deck. Keep you log book, change of cloths, and anything else you want dry in the dry bag somewhere besides below the seat, cause that area gets wet.
When ready (this could be on the trip out/at the dock/or when instructed) get your gear together. Attach the BCD and Reg to the tank, check your Pressure, pull you fins out and put them under the seat, get your mask together (defog/snorkel if you dive with one). Some like to put their mask in the rinse bucket, as it prevents them from getting stepped/sat on.
When you get about 10 minutes from the site, the DM should tell you to suit up. Now is when you put on everything, and get ready. Suit, booties, computer/dive watch, fins, and crawl into the BCD sitting down. Make sure you have everything you want to dive with before getting into the BCD.
Many people (myself included) put on the bottoms of the wetsuit, and booties prior to the 10 minute call. You may want to do that at the dock if you have problems getting in a wetsuit. When the 10 minute call is given, then you just have to get your top half in.
Pay close attention to the Dive Briefing. Make sure you and your buddy agree on the procedure if you get seperated. Generally one minute look about, and surface to hook back up.
Make sure to check air. Most DM do so as well, but don't count on that. Make sure your equipment is together before entering the water. IOW's fins straps tight, reg in mouth and breathing, BC Inflated, SPG hooked onto the BC, etc.
Common problems I saw when boat diving.. people forgetting to change out there tanks between dives. Air off (generally caught by DM), Loosing mask when entering, having loose gear hit them in the face when entering (loose 2nd in this case).
Don't rush, do a buddy check, and go over your basic UW signals with your buddy if needed. Stay calm, dive Safe, and Have fun!!