you will normally find the first day that they will offer some specials or give away extra minutes for signing up the first day.
Also look out for a drawing for free minutes.
The service is pretty good but can be very slow. You should have access in your cabin no matter where you are, but at the worst case, you can go to the Internet Cafe (on all ships) and set up there.
There are a few sites available for free, such as Carnival.com.