From the United States, your party can dial toll-free... 888-DC-AT-SEA (888-322-8732). If the party calling you is outside the United States, they'll have to dial direct +1-732-335-3281. They will need to know which ship you're on and your cabin number.
Make sure this is used for emergencies only, because you will be charged somewhere between $7.50 and $9.50 per minute for the incoming call.
A cheaper option is email. Create a Hotmail.com account to use while you're on the cruise. Give the address to those folks you want to keep up with on a daily basis or so. Your cost will be $0.75/minute.