Get a taxi from the airport -- about 20 minutes and BZ$50 to reach Belize City.
There are two water taxi services and each has their own terminal in BC. Have a printed copy of the schedules (see websites) with you so you can see which service has the next boat going. Tell the taxi driver to go to that terminal. I don't think there's enough difference between the two services that would make me want to wait for the next boat from one particular service.
It's about 1 hour to CC, and another 15 to 20 minutes to AC.
Fun. Not really, but an experience. Basically it's a bus on water. I always thought they should be called water buses, not water taxis.