From a Resort
If you are staying on Paradise Island, Atlantis Resort, most of the resorts are in walking distance to the Blue Lagoon ferry entrance or you can take a quick taxi ride, $5 each way. If you are staying on the New Providence / Nassau / Cable Beach, you can either take a local taxi, about $20 each way plus $1 toll. You can also have Johnson Bus service pick you up at your resort, $12 round trip (you will need to request this on your reservation form).
From a Cruise Ship
You will take a taxi which goes over a nearby bridge to Paradise Island. Taxi will take about 10 min, and cost around $10-$12 or so plus $1 for the bridge toll. There are plenty taxi waiting for you at the cruise ship dock.