I've done a few, all for my old boss on a Swan 53', MA to St. Thomas.
Unless you are the captain, where you will need USCG licences and whatnot, there isn't much needed in the qay of qualifications aside from sailing experience. Your first trip is likely to be unpaid except for expenses to get some miles under your keel. Once you can say that you've done it and make some connections that will invite you to go again on other trips it will build from there.
Whoever the guy who got $1400 for 4 days is, I want to work on the boat he was on. Typical pay for delivery crew is $100/day plus expenses/flight.
As for the actual experience, it is both fantastic and awful at the same time, depending on the weather, boat, and other crew. If the weather is nice, the boat in good condition, and you get along with the other crew, it is great. I have great memories of sitting on the foredeck on a 2 AM shift with a cup of tea on a gorgeous warm night, 400 miles from anywhere, watching the dolphins swim along with the ship (you see the bioluminescence of where they are and see them as they jump across in front of the bow). I also remember being horribly sick standing in the rain and cold having to hand steer the boat in 25kt aft quartering seas after having basically no sleep, and then having to fix something that breaks.
The last trip I made, last fall, we had to run into Bermuda to shelter from a tropical storm, we came in with 10-15 foot seas. After being in Bermuda for 4 days to ride it out, we left and had nearly no wind all the way to St. T. The total trip I was away from home for nearly 3 weeks.
I'd do it again on the right boat with the right people, but don't expect to get rich from it.