You can get certified on a trip. The course would take up most of your vacation, probably five days. In resort locations like Cozumel, you can also take a an introductory one-day course that does not lead to certification. It is called a "resort course," or "discover scuba," or something like that. Typically, you will spend the morning in a pool learning some of the basics and then in the afternoon they will take you out for a shallow (30 feet) dive in the ocean under close supervision of an instructor. It can be a great experience, but like many other things, the quality of these courses varies widely. My first diving experience was in a resort course. We received good instruction, the dive was conducted safely, and we had a great time. It got me really interested in scuba. I have heard of courses with little or no instruction and unsafe practices. People who take these courses can get really turned off.
I don't know who runs a good resort course in Cozumel. I would recommend staying away from Aquaworld. It is a big watersports operation in Cancun that has a Cozumel location. I have heard some real horror stories about them. Some of the other people on the board may be able to help. If you post a request for a recommendation in the Cozumel forum, you may get some helpful responses.
Five things for a first timer? (1) The first rule of scuba: always keep breathing and never hold your breath. You should always be inhaling or exhaling. (2) Everything in scuba is on "island time" - really slow. Take long, slow, deep breaths, move slowly, don't kick constantly and go racing around. (3) Don't touch things (coral, animals, whatever) underwater. (4) Equalize your ears early and often. "Equalizing" refers to equalizing the pressure you feel in your ears as you descend. You can feel this in a swimming pool. Equalize on the surface before you start a descent and then equalize every foot or two as you descend. If you wait until you can really feel it, it is too late. Equalizing is a big topic. They should cover it well in a class. If they don't, you probably shouldn't dive with them. (5) Nothing the water is going to bite or sting you if you leave it alone and don't get too close. Don't worry about sharks, sting rays, barracuda, etc. The one exception is little jellyfish, which can just drift by and sting. It doesn't happen very often and it's not usually too bad. It stings, but can be remedied with a little vinegar and goes away.
I need to add a sixth: keep warm. If you can rent a wetsuit for this, do it. The water seems warm until you spend a couple of hours in a pool. Then your lips turn blue, you shiver, and it's impossible to pay attention or enjoy your self.
"Booties" (neoprene wetsuit boots) are necessary to use open-heel fins (the ones with straps on the back). There are also full-foot fins (the ones that go on like a shoe). If you have ever used snorkeling equipment from a hotel's watersports operation, you got full-foot fins. If you use the equipment they give you for a resort course, you will get full-foot fins. Full-foot fins are usually worn over bare feet. You can also get booties that are more like a neoprene sock that can be worn with full-foot fins, mostly to keep your feet warm. I would not buy booties for a resort course. They need to be fitted with fins to be usable. If you like the resort course and decide to take the classes to get certified, you will need to buy gear, and what you bought for a resort course may not be what you really want.
Good luck, and enjoy if you decide to do it.
