You can take your laptop but unless your ship has a wireless router and you have a wireless card you won't be able to connect to their network. Even if you are able to, you'll have to be within a certain range for the signal to transmit.
I'm not sure if you can hook up to the phone in your room, but it will cost you a small fortune if you do...and maybe your 1st born.
You can go to the internet cafe and buy blocks of time on their computers.
I took my laptop with me when I cruised on the Glory in March...whether or not you should bring a laptop while on vacation is a topic for another thread, but some of us have to stay in touch with the office or the real world. I had my own wireless card (they also rent them, and laptops as well) and the whole process was very easy...if you are not running Windows XP, I understand that you have to load some special software, but since I have XP, it was totally painless. I believe I paid about $55.00 for a block of 100 minutes, with no refund for unused minutes. The speed was not bad; not great, but not bad and you had to be either in the Internet Cafe or the adjoining lounge to get a signal...I had visions of sitting in my cabin in my underwear checking email, but unfortunately that was not possible. I'm not sure if you could use dialup from the cabin, but as a previous poster mentioned, that would be extremely expensive. For email, I was able to use my ISP's Webmail service (Hotmail, Yahoo, etc. would work the same way), but I couldn't use my Microsoft Outlook to send and retrieve email.