You can advance purchase minutes of connect time in various "blocks". The more minutes you purchase at one time, the lower the cost. However, be advised that it is still very expensive, and slow ... Additionally, there is no credit or refund for unused minutes.
Here's what I got from their website -
"Internet access is available on all Princess vessels through our 24-hour onboard Internet Cafe and wireless network -- which is available in staterooms and various public areas including our world famous Piazzas.*
Use our state-of-the-art computer systems to access your web-based email account, or browse the Internet for world news, sports and stock trading. Or bring your wireless-enabled laptop and access the Internet through our onboard wireless network.
Passengers who subscribe to email services from an Internet Service Provider (ISP) are advised to verify that their ISP has a web-mail viewing site prior to sailing. Most major ISPs have websites that allow email access via a web browser using an email address and password.
Please contact the Internet Café Manager onboard for information regarding the charges that apply to Internet and wireless services and any other specific requirements.
Plus – Platinum and Elite Captain’s Circle members benefit from credit toward Internet Café packages while full suite passengers also enjoy complimentary Internet access.
* Internet access via satellite is significantly slower than high-speed connections on shore. Princess Cruises reserves the right to filter content accessed via the ship's Internet services. Please note high bandwidth consuming applications such as voice over IP telephony, peer-to-peer file sharing and streaming media may be restricted onboard Princess vessels."