Xine is a very popular multimedia player for Linux. Above all, it's a movie player, but it also can play audio files or connect to live streams. DVB cards can be accessed using the dvb input plugin.
Xine in its graphical version gxine for X11 has a very intuitive and powerful GUI. Many users like it for providing much functionality for watching TV very easily. (On the other side, VDR has better functionality for recording / scheduled recording, for the price of more installation and configuration fiddling.)
In Debian/Ubuntu etc
apt-get install gxine
Then create the channels list using the dvbtools' scan
mkdir ~/.xine scan >~/.xine/channels.conf
Now start up gxine
and open the DVB card with
File -> Open MRL -> dvb://
You should now see a program. You should be able to zap around using the NumPad-9 / NumPad-3 keys, the xine playlist, or using the next/previous chapter buttons in your gui.