This How-To assumes that you can compile additional kernel modules, and use the lspci and modprobe commands. You potentially will also have to know your distributions's mechanism for auto-loading modules on boot.

After you have installed the card, the lspci command should display the following 2 new entries for the card:
02:09.0 Multimedia video controller: Brooktree Corporation Bt878 Video Capture (rev 11)
02:09.1 Multimedia controller: Brooktree Corporation Bt878 Audio Capture (rev 11)
To install the modules, and set up XFree:

1. Compile the following modules for your 2.6.x kernel (unless you already have them).
Device Drivers  --->
     I2C support  --->
           I2C support
             I2C device interface
     I2C Algorithms  --->
          --- I2C bit-banging interfaces
           I2C PCF 8584 interfaces

     Multimedia devices  --->
           Video For Linux
     Video For Linux  ----->
          Video Adapters-
           BT848 Video For Linux
2. If you compiled new modules, reboot and see which modules modules are now auto-loaded. The correct ones may already be loaded now (They do on Gentoo with sysfs/udev).

lsmod (and look for the following:
video_buf              16644  1 bttv
i2c_algo_bit            9096  1 bttv
v4l2_common             5120  1 bttv
btcx_risc               4104  1 bttv
videodev                7424  1 bttv
i2c_core               18692  6 i2c_dev,bttv,i2c_algo_bit
If you have those then you are good to go!

If not, then modprobe any missing modules and alternatively add them to your distribution's module-autoloading script. For Gentoo : /etc/modules.autoload.d/kernel-2.6 and for Debian: /etc/modules

3. Add v4l to your XF86Config

open the /etc/X11/XF86Config file with you favourite editor and add the following to the "Module" section:
#       # Video For Linux
        Load    "v4l"
You will have to reload XFree at this point.

That is it! Very simple install.

For Television viewing, I recommend TvTime

Pror to setting this up on my workstation, I read this Newsforge article.