A 'data port' doesn't sound as 'dial-up'. With dial-up you use your normal phone, and you need both a dial-up modem (a 56K6 modem, mostly, that's the speed) and be registered by an ISP that lets you phone in and specify your username and password.
A 'data port' sounds as an Ethernet-connection. Check if your laptop comes with it. It might be called 'network connection' or 'LAN connection' also. You need a socalled RJ-45 cable to connect the Ethernet outlet offered by the hotel to it.
If your laptop doesn't have such a connection (but all current ones have it) and the hotel doesn't offer wireless, it's hopeless.
You better contact the hotel for the details. Is it Ethernet, do they provide a cable to use, and if not, do you need a crossed cable or a straight one?
Hope this helps.
I am going away and taking my laptop. The hotel has a data port.
At home I use wireless cable to connect so I have no idea what to do to use the dial up.
Could someone help me out?