Most new HDTV's (Plasmas, LCD's, etc) have either VGA or DVI (DVI usually in the form of HDMI, but there are DVI-HDMI adapters out there) inputs. I hooked my laptop to our Plasma TV and it worked fine.
If the TV is older and only has up to Component (RGB), you can often use RGB with your graphics card. Usually this comes in the form of a 7-pin S-Video cord that has Red, Green, and Blue RCA plugs on it.
If you TV doesn't support Component, and only supports up to S-Video, you can use an S-Video cable to go from PC to TV. Usually laptops have S-Video ports for their TV-out, so it should be simple.
If you only have composite, then you'll either have a composite (yellow) port on your PC, or you'll have a 7-pin S-Video (standard S-Video uses 4 pins, the extra 3 work with special adapters to provide composite and component jacks). If you have a 7-pin S-Video port, then your PC should have come with a yellow plug that had S-Video on one side and composite (yellow) on the other. Use that to connect the TV.
Usually you can find the software options by right clicking, Properties, then Settings tab. Usually you either extend your Desktop on to a second monitor or click the Advanced tab. If you use nVidia or ATi's newest packages, there will be an option (Catalyst for ATi, nView or something for nVidia) in your right-click menu already, just use that option instead.