Looks like it has been supported since kernel 2.6.27
Plug it in, make sure it is found and firmware is loaded. Example
dmesg | tail
[ 4041.795122] DVB: registering new adapter (Pinnacle PCTV HD USB Stick)
[ 4042.367111] usb 1-10: DVB: registering adapter 0 frontend 0 (Samsung S5H1411 QAM/8VSB Frontend)...
[ 4042.367221] xc5000 6-0064: creating new instance
[ 4042.367727] xc5000: Successfully identified at address 0x64
[ 4042.367731] xc5000: Firmware has not been loaded previously
[ 4042.367739] Registered IR keymap rc-dib0700-rc5
[ 4042.367845] input: IR-receiver inside an USB DVB receiver as /devices/pci0000:00/0000:00:02.1/usb1/1-10/rc/rc1/input12
[ 4042.367918] rc1: IR-receiver inside an USB DVB receiver as /devices/pci0000:00/0000:00:02.1/usb1/1-10/rc/rc1
[ 4042.368104] dvb-usb: schedule remote query interval to 50 msecs.
[ 4042.368110] dvb-usb: Pinnacle PCTV HD USB Stick successfully initialized and connected.
You'll need linuxtv-dvb-apps installed. If not look in your repo for it.
Scan for channels with a scan utility to make a channels.conf file for whatever media player you use, from whatever tv signal source you use. Example
scan /usr/share/dvb/atsc/us-ATSC-center-frequencies-8VSB > channels.conf
Then put that channels.conf file where your media player can find it. Example
Play the channel with your media player. Example
scan, wscan or dvbscan is in linuxtv-dvb-apps
There are also a half dozen apps for playing TV like Myth TV.