I have several friends that do it and my wife and I have gone with them on occasion. We've received offers but have declined so far.
Pay's not all that good ($600-$800US/couple/week I seem to recall one offer we had about 6 months ago for 3 months on the Eastern US seaboard)but all your extras are covered (food, travel, accomodation, etc.). So if you're just wanting an experience...
There are several ways to go about this. T2 mentioned contacting the steamships directly. That might work but it could also be a dead-end if you contact the wrong people. E.G. My impression is that dance teachers on Princess are controlled by one couple out of England. (I'll see if I can find their contact later. Not sure where I've put it). If you contact the lines it might be worth asking who handles hiring of dance teachers.
A lot of lines now use a talent agency to supply them teachers. I used to put a lot of Dance Hosts on cruise ships. Mostly I supplied them through:
http://www.sixthstar.com
You could also try:
http://www.toseawithzee.com
I hope that's the right URL. If not Google "Diane Zammel" or "To Sea With Zee". (Being Canadian I think it should be "To Sea With Zed"

)
Unfortunately, most common with these talent agents they want you to pay them about $25/day to go. That's not neccessarily a bad thing though as it gets you on board and your name gets known. Then the paying gigs might start coming.
That's what happened for our friends in a sense:
They organized their own group (21) and booked time for private dance lessons on board a 7 day cruise in Mexico (Royal Carribean). As our group was small they let the cruise director know they were willing to open lessons up to all passengers. They gave 3 group lessons.
When they got home the phone was ringing. Offers for 3 and 6 months paid gigs. They said they could only go 1 month at a time. The lines opted for that and they go 1 month twice a year now.
They usually do one trip as employees and one like the talent agencies above so they travel more like passengers.
Generally, you teach a one hour group class every sea day. Not all lines require a performance. Given a choice between going as an instructor or a dance host I'd go as an instructor. Dance Hosts start around 6:00pm and go until 1:00 am (you get breaks). However, I get reports from some of the people I've sent about demeaning and demanding activity directors. My impression is instructors are treated more as professional artists.
A troubling trend we've noticed lately is some ships no longer take professional dance instructors. Instead they pull a performer out of the chorus and have them teach a group class.
We were on a Carnival boat about a year ago. My wife and I teach International. There was also an American Style instructor on board we befriended. We went to the "cha cha" class to help out. The person teaching taught no steps either of us recognized. If anything it was closer to Mambo or Salsa.
On a Royal Caribbean boat the activity director who taught the chorus taught group tango as danced by Groucho Marx.
The boats seem only interested in providing any activity over substance.
OB