If you set up an online email account such as Yahoo or Hotmail before you leave home and give your family your email address, it is very easy to stay in touch.
There are no internet 'cyber cabins' on Princess but they do have an internet cafe onboard. We are platinum members so there is no charge for us but I think it ran somewhere between .50-.75 per minute for use. Also you can rent laptops at the pursers desk 24/7 if the internet cafe is not open when you need it. You have to stay close to the pursers desk with them though and they do not work from your cabin.
Returned from cruise and thought I let people know how the E-Mail worked on the Grand Princess. Charge was $7.50 for the first 15 minutes. Their system is not very fast, it will take you the first 5-10 minutes to get used to the system. First 2 times I tried to e-mail they never got to their parties. I was in cancun and found a place to e-mail for $1.00 for the first 30 minutes and everything went well. Ship system never went through.