In addition to the internet cafe,
Infinity and Summit offer Internet access in every stateroom for those who bring a laptop with a modem connection. The service is available at a daily, weekly or per minute rate.
You may also find internet cafe's on shore, close to the piers, usually cost a lot less than onboard, have used them in the past and are around $5 for an hour.
If you bring your own laptop with modem as Donna commented you can sign up for the complete cruise duration of $100.00 in the cabin. The cabin steward or onboard computer guru will hook it up and configure if the instruction sheet is confusing to you.
I did this on a recent cruise on the Summit. Much cheaper in the long run than the onboard internet cafe. Not positive of the per minute cost but I believe around $1.00 a minute. Time passes quickly on a computer so charges can mount up fast.
__________________ Ready to Steer towards another cruise