A regular TV display has around 640x480 resolutions. Many video cards in computers don't go down to 640x480 any more. 800x600 is a common starting point, hence such computer resolutions simply won't work on a normal TV. To overcome such problem, you can use one of the following solutions:
Using S-Video Connector:
If you can take your computer down to 640x480, you can try connecting it to your TV. Many laptops actually include an "s-video" out for exactly this purpose. Depending on your laptop it may be treated as a mirror of your laptop display, or as a second monitor, or you may be able to switch between them.
Using Converter Box:
If S-video is not an option, there are converter boxes available that will take a standard VGA connector and turn it into a composite video signal that can be plugged into a TV with a composite input.
In both cases, video playback (movie, video songs) looks quite good while reading email or surfing the web is of poorer quality.
For better surfing and other internet activities, it'll require a new digital TV. Newer TV's are going HDTV (High Definition Television) with digital (DVI) input. The TV has higher resolution than traditional television systems which may not support the same higher resolutions that your computer monitor might, but they'll almost certainly support resolutions that are much more acceptable for computer usage.
Using Television as a Second Monitor:
For using television as a second monitor i.e. to mirror what's going on in your primary computer screen, many laptops support using both the internal LCD screen and the VGA (or S-Video) output at the same time, so you may be able to see same stuff both side. If you don't have that option, you'll need to get a splitter of some sort that will allow you to take your computer's monitor output and send it to two different devices: your regular computer screen and a VGA converter box as I described above. Alternately you could purchase a video card that supports TV-out, or supports dual screens.