There are several options:
1) Fly into Orlando ( MCO )
2) Fly into Melbourne ( MLB )
3) Rent a car
4) Use the cruise line shuttle
5) Hire a public shuttle
How you proceed depends on what your plans are. MLB is closer than MCO. Delta flys into MLB, however, Delta is having labor problems.
Are you planning to spend some time in or around Orlando? If so, a rental car might be your best option. You have more control over where you are going and have a place to store your bags. Budget, Avis and Thrifty (and perhaps others) all have rental locations in both Orlando and near the port.
The cruise line shuttle is always an option. When I checked for my cruise on the Glory at the end of this month it was $25 per person each way. I am arriving two days early, so from the airport to the port this was not an option. Returning I have an evening flight, so I am renting a car so I can go where I want and store my bags.
Many people like Art's Shuttle. Here is a link --
http://www.artsshuttle.com/
You might also get more info/options from this link to Orlando & Port Canaveral transportation services ...
http://www.orlandotransportation.net/