If you're talking about right now, many boats have already departed for their hurricane
season destinations (Trinidad, Grenada
, Rio Dulce, East Coast
US). They normally head
north from St Thomas, Tortola or St Martin/St Maarten, some from Antigua
, in early May. If going south, they just work their way down through the islands during May and June.
Finding a berth will be mostly a stroke of luck if you're just walking the docks. I think you'd be better off checking the various Internet
crew-seeker sites and contacting the skippers directly.
And just a caution--you'll find it
impossible to fly in to any of the islands with a one-way airline ticket, unless you have a letter from a boat captain
stating that he will be responsible for your transportation off the island. Otherwise, you'll need to have a return flight booked. The C&I folks will also want to know where you plan to stay on the island (hotel or whatever), and will definitely raise their eyebrows if you say, "I don't know yet, but I'm looking to find a boat that will take me on as crew."
Best of luck.