This will really depend on the chip on your card. I have a tv tuner which has a BT878 chip in it - which is very common - these will probably work with linux. You may need to carry out a visual inspection of the card to find out what the chip is, or read the specification on the ATI website or in the manual.
I'm guessing the card is plugged into the computer because you used it on windows. Open up a terminal and type:
If a device like video0 exists, you might be in business here. If the device doesn't exist, search through the /dev directory and find a video-like device. If you cant find one you might need to compile the kernel module for this (yeah - it sounds daunting but once you have done it for the first time, it will be easy). There are some good guides for this around - check the Tutorials section.
Next, you might be wise to run a quick test on the card. I use VLC for this, as it can get the signal from the video0 device. If you want to do this, you need to install the VLC package. Something like:
sudo apt-get install vlc
If the package is not found then try:
apt-cache search vlc
and see what turns up.
Once it has installed, open up vlc (just type it in the terminal window) Click file and select open capture device or just press ctrl + a. Type video0 or whatever your device was shown as in the /dev directory. Click open.
If you see a load of white noise stuff or even a signal, your card is working.
You can then install a more advanced package like mythtv or tvtime (or even both) which should be able to store channels and pick up tv listings.