It's quite easy. Most ships have a daily newsletter with news, headlines, selected stock quotes and sports scores. While most ships now have telephones in passenger cabins, you can also call someone on shore through the ship's radio operator while at sea. And, you can make phone calls from most ports. In addition, most ships have fax capabilities. Many ships have televisions in the cabins, complete with CNN and a host of other channels. And, depending on the strength of your cell phone signal, you may be able to use your cell phone while the ship is in port.
Many cruise ships also offer prepaid internet access. Some even offer this within each cabin!