Yes there is and there will be a pack in your stateroom explaining how to register but it won't be cheap. As they have a laptop coverage will be in most areas of the ship you will no doubt see the link boxes as you go about the ship with the one/two aerials protruding.
Had a look around the various websites and $60 for 3 hours for surfing seemed to be an average. Look for bundle options when you get on board and you look further into this for your kids. Cheapest is to stick to just emails.
Any internet use onboard ship, whether you use your own computer or not will be expensive. That is how they make money out of passengers! Don't forget that all communications onboard ship are by satellite, and are thus very expensive to access. Happy cruising.