After arriving, you can depart to San Pedro from the same airport. You can reserve your ticket on-line (see websites below). Flight time is less than half an hour. What could be easier?
Or you could taxi to the Municipal airport in Belize City and fly from there. The advantage is that tickets are cheaper, but you'll have to calculate your costs taking into consideration air fares & taxi fares.
After arriving, grab your luggage and get a taxi (maybe 2 taxis for 5 people) to one of the water taxi terminals in Belize City. Buy tickets and wait for the next water taxi. Spend about an hour getting to San Pedro.
Here are the relevant websites with schedules & fares. A taxi from the airport to BC costs BZ$50. This should allow you to calculate your costs.
Maya Island Air, http://www.mayaregional.com/
Tropic Air, http://www.tropicair.com
Caye Caulker Water Taxi Association:http://www.cayecaulkerwatertaxi.com
San Pedro – Belize Express Water Taxi:http://www.belizewatertaxi.com
Consider flying over, and returning by water taxi.