You will have service when you board however once you are 3 miles out to sea you will be into International waters and data roaming will kick in - this can prove very expensive so we recommend either switching to airplane mode or purchasing the cruiselines internet plan. Click here for cruiseline wifi pricing.
Most cell phone providers offer an international call/text plan - for example AT&T's runs $10 per day when you use it.
Most cruiselines offer a mobile app that you can use while onboard the ship, some offer robust texting and calling (to other phones onboard)for a minimal fee others simply offer onboard activities etc.
Ship to shore calls from your room are quite expensive, sometimes upwards of $9 per minute.