As PW305 said it's pretty straight forward. I'm not quite sure about the operations at Montego Bay but if you'd like you can have a look at the FBO's website here for contact info. Welcome to the IAM Jet Centre: Montego Bay, Jamaica
I work at the General Aviation Centre in KIN and its a breeze once you have everything put together. AJAS and Jamaica Dispatch Services are our two main handlers and will provide fuel, ground carts etc and even look about your Immigration and Customs forms for you so long as they're given a decent heads up. I suppose if you should use the service providers listed by the other posters above it should be even more painless. Arriving in KIN you can expect to park at Gate 11 and if you're staying over 5hours there will be parking fees assessed based upon your aircrafts MTOW. If you're staying over-night or more than 5-6hrs you'll be repositioned to the military ramp to free up the space by Gate 11 and 12.
As for the cities Montego Bay is the tourist mecca of Jamaica and Kingston the largest city/capital & the business hub. In Kingston our two authorised very repuable taxi services are JUTA and JCAL. Hope that helps!