Where in the Gulf are you going to be diving? I have dived off boats in the Gulf a few times. I have mainly gone out of the PCB area and most of the boats in that area are bigger "cattle" boats. On these boats you pick a spot and put your gear together. Once all your gear is together get your wetsuit on up to your waist. At this point get anything that is not going in the water with you picked up and put away. On the way out you will end up chatting with the DM/Instructor/Captain a few times. They like to chat with people and they like tips. Once you reach the site the DM/Instructor/Captain will do a bounce dive to hook into the wreck and while he/she does this you go ahead and get your suit on the rest of the way. DM/Instructor/Captain will get back on the boat and start the briefing with conditions first and then the expectations of the boat. When the briefing is done you will sit back in your spot and get all your gear on and checked with your buddy. Air on, regs breath, air in BCD, computer on and mix correct, everything securely attached as it should be. Then walk over to DM/Instructor/Captain that is at the launch side of the boat, hand him/her your fins and then lift a foot backwards. DM/Instructor/Captain installs first fin and slaps bottom of your foot, you raise other foot back and the process is repeated. At this point you are ready to splash, you are given the go ahead and you splash, give the OK potato on your head signal and move on so the next one can come on in.
Couple things, first, this has been my experience with charters out of PCB and they have been great experiences, not ALL boats will do that exact process but the majority should be close. Secondly, you saw how I would say DM/Instructor/Captain. I did that because the charters I have been on the members of the crew had numerous positions regardless of what they actually did on the boat. One trip, the boat had two Captains and three instructors on, there was not a single DM working on that boat. One of the captains was actually the bounce diver that tied us into the wreck and the usual DM position helping with fins and getting people off the side was an instructor. So do not assume what someone is based off of what they are doing and be respectful to all.
In closing, relax and enjoy yourself. A good crew will naturally put you at ease and have you a boat diving pro in no time.