It's really easy to connect your computer to your TV. There's only a couple things you need to know:
Remember that a common TV has much worse reception than a common computer monitor. For this reason, if you don't have an HDTV, I wouldn't even attempt to hook your computer to your TV. The results will not be pretty. You need to make sure that your TV supports a resolution that your computer can display. For instance, if you have a 1080p TV, then make sure your computer can provide a 1920x1080 signal to your TV.
Check the back of your TV. You need one of these kinds of connectors:
If your TV has this type of connector in the back, you're in luck! This is the standard display connector that most computers use. You should be able to get a standard VGA cable which connects from the back of your computer to your TV. That's it, voila!, you're done! VGA isn't the absolute best quality, but it's still so good you probably won't notice it. Still, f you're concerned with getting the absolute best, you'll need a TV that accepts either DVI or HDMI. Also note that you'll have trouble playing copyrighted content since these types of connectors don't support copy protection. Of course, you can always use a program like SlySoft's AnyDVD to bypass copy protection on DVDs if you don't have HDMI.
(note that you want the VIDEO IN, not VIDEO OUT that's shown in the picture)
Component video, as far as I understand, is a bit better than VGA. The problem is that no computer supports it out of the box. If you buy a graphics card, like my beloved XFX 8800GTS for instance, you can write XFX customer service to send you a special adapter that will allow you to output component video. The shipping and part are usually free; all you have to do is ask. Again, this form of cable doesn't support copy protection.
A DVI connector would fit the cable shown above. This is the best in terms of quality, but it doesn't have HDCP (HD copy protection), so you will have trouble playing copyrighted DVDs through this cable.
HDMI is basically the same quality as DVI, but it has built-in copy protection so you can play copy-protected DVDs legally. It also allows you to transmit audio through the same cable, which can help cut down the clutter. This is "the state of the art".
Connectors that won't work
If you have any of the above connectors, you're in good shape. But any other connector will probably be difficult to get to work..