Not knowing how much experience you have, I'm going to suggest a couple of routes. The first is if you are not very experienced. The bigger the boat the more crew it takes to sail her. This is doubly true of coast guard certified passenger vessels. They have to have a certain number of crew members on every trip. Offshore trips normally require double or triple the amount of crew needed to sail the vessel. When we took the Liberty Clipper down to the keys, we hire a couple people who didn't know forward from aft, literally. We just made sure that when we needed to do any major sail handling, we would do it on watch overlap.
May, could be just a little bit late to catch a ride north, you'll just have to call around to see when all the wintering boats are heading up again. Liberty Clipper, Appledore, Harvey Gamage, HMS Bounty, and the SEA boats are a few that I know of that spend the winter in the south, but I'm sure there are plenty of others. Just before they head north, they start hiring more crew so it's easier to get on board at that time. Take some time to look at http://www.schoonerman.com/
, this site lists most of the tall ships, as well as what they do.
If you want to try this route, you should make up a resume, include what experience you have but don't focus on it, tell them a little about your self and such. Send the resume to the HR department if they have one, the main office if they don't. Then call them about a week after you send the resume, make sure they got it and sweet talk the staff a bit. They're not as worried about experience as most people would believe. In fact, we usually had more trouble with the ones who had a lot of experience on twenty and thirty foot boats. Each of our head sails had more canvas then most twenty foot boat had in total. Yet these guys would try to handle the lines like they were out on the lake in a Catalina. Inch thick sheets can remove fingers if you don't handle them right. Don't take off as soon as the trip is over either. A cruiser docks his boat maybe twice a week, but working vessels dock two or three times a day, in all kinds of weather as well. same for sailing, you will learn how to sail and dock under good and bad weather a lot faster if you are going out irregardless.
The other option to get on a boat going north or to Europe is to try the crewing agencies I listed before. But if that doesn't work, head down to the American Virgins and pick up what ever jobs will keep you close to the marinas. Fish mate, deck hand on a day sailor, or even bar tending at the waterfront bars. Then tell every body you talk to what you want to do. There is always a boat that has a crew member pull a no show, or one who gets fired for some reason, or even a crew member and captain who don't get along. This last one can be a simple matter of different opinions. I knew some people who were rabid Republicans, Democrats, Christians, environmentalist or some other thing that just didn't make it easy to sail with the opposing parties.
In regards to living in really close quarters with other people, there are a couple things that you can use to determine if you up to the challenge. Did you grow up with brothers and sisters who shared rooms, or spend time in an army barrack. Its a lot like that. You need to be able to withdraw into yourself for periods of time with out being able to leave the company of others. If you get the option, pick crewing with sailors that have been at it for a long time, they will be better at disappearing into themselves and will be more attuned to the moods of their fellow crew members.