Should be no problem, if your GSM account is data enabled - most will do this for free, just ring them up.
I've used an IR connection via a Nokia 8310 to connect to an ISP - works fine but limited to 9,600 kbps. I used a USB-IR adaptor. If your phone has a USB port, then you could just connect it directly. You just need to install the phone as a modem and if necessary add the IR serial port drivers - then just configure dial-up networking as for a normal modem.
If your network provider supports HSCSD (and you subscribe to it), then you can get connections of up to 43.2 kbps (43.2 down, 14.4 up). There is usually a surcharge for this mode. My provider surcharges £0.25/min for a 43.2kbps connection (reasonable I suppose as you are using 4 GSM channels).
Nokia provide a seperate control-panel applet for configuring the speed of the 8310 modem. A simple slider goes from 9,600 to 43,200.
The alternative (if supported, and if you subscribe) and faster way is to connect using GPRS as your internet access (you don't connect to your ISP, instead your network provider acts as ISP). This type of connection is always on, but is charged per kilobyte. I've not tried GPRS because it is WAY too expensive (at £0.07 per kB - someone is taking the mick!)