If you've never had a tan before....could this be due to your skin-type? I know some of my dearest Irish-American friends only get beet-red during summer, but simply can not produce a tan.
If not, then you can begin going to a tanning salon. The clerk will best be able to advise you on frequency and strength etc. You will most likely have to commit to every other day for a few weeks all the while increasing the amount of time you are in the booth/bed. It's a very controlled situation but best for those who do not wish to burn on thier first day in the Carribbean sun!!
I usually start my tanning-before-a-vacation about 2 weeks before and I go about 6 times in that time. I tan often and well, however, so your experience may be different.
I go to the tanning salon once a week starting about a month before cruise, then twice a week the week before cruising. I get a nice base and then no burn, you may want to give that a try for no more than 10 minutes and see how you do, you sure don't need to go on a cruise and get sun burned, its not fun at all.
Also, remember that once you are cruising, still use a high spf, the sun if very strong down there and you may not feel it at first.
Even my husband (who tans easily) goes to a tanning booth a few times prior to vacation to get a "base" tan because the Carribean sun can be brutal compared to Minnesota! I'm more fair, so I start about a month ahead of time and go sllloowww! I buy an unlimited month package so I don't feel like I'm wasting my sessions when I only go 10 min in a 20 min bed. The gals laugh at how quickly I'm in and out, but I don't let myself burn and never increase my time until I can handle it without getting pink. If you have NEVER tanned, you may need to start at less than 10 min even. Good luck!
Use sunscreen and stay out of the sun during the middle of the day. Watch yourself carefully at other times and cover up as soon as you start to turn a little pink. Sunscreen does not prevent a burn, it just means you can stay in the sun longer before you get one. Personally, I am afraid to try a tanning salon. Have a great time.