you can do it one of two ways,...
1) Digicel has a pretty cheap phone and pay-as-you go service. You buy the phone and sim, under $40US and then 1000 international minutes which last time I was there that was $1000JA. You then keep the phone and if you top up online at least once every three months, you get to keep the phone and number (this is what I do, I've had the same number for 2 years) if you go often or every year....
2) If you already have a cell (and it is fairly new) then have it unlocked, purchase a sim ($400JA about) and then again purchase the international minutes. Again, you can top the number up online while off the island and you keep the number. Your own phone (from the US) is more then likely locked to the service provider so to unlock it, call them or send them an email asking them to unlock the phone at least a few weeks before you go.... or, you can get it unlocked on the island for about $2000JA. You then just pop in the JA sim each time you want to make a call.
I use my JA phone a lot when I am there and I go a few times a year so I want to keep my number but if you are going for a one-off, then option 2 is your cheapest way to go (no new phone). I had a phone from a plan 2 years ago, had it unlocked, purchased a sim, and then I purchase minutes while I am there and every 3 months when I am home to keep the number active.
There is sometimes one more option. I know of a few drivers and hotels in Negril that actually have a few phones for rent which you then only need to top it up with the appropriate minutes (local and/or international)...but not sure if there is anyone in Mobay that does this but would imagine there is.
Here is the site for Digicel (don't go with Lime) so you can see the cheapest phone...
http://www.digiceljamaica.com/
Hope this helps....message if you got questions
Sorry forgot to add the option 2 won't work with an iphone...my previous phone is a blackberry, the phone has to take a "normal" sized sim for option 2 to work. Also, Digicel has a few stores in Mobay and other places (there is one in Negril) for you do purchase the phone and sim. Minutes can be purchased all over the place.