It depends a bit on what kind of video card you have and what kind of input connections are on your TV. Modern video cards have both a traditional analog VGA connector and the newer digital DVI connector. The latter is much wider than the VGA connector and has a much different pin organization. Your card might also have a round S-VGA adapter, but that won't help for video in high-definition formats like 720p.
Your television probably has an HDMI connector and may also have a VGA input as well. If you have an HDMI input on the TV and a DVI output on the video card, you can use an DVI/HDMI
converter cable. If they both have a VGA connector you can use a VGA monitor cable instead. People debate about whether one method has higher quality than the other; I don't see big differences in practice.
As for audio it also depends on what kind of sound card you have and the types of inputs supported by your TV or audio receiver. I just use the Intel audio chip on my motherboard and connect the computer to my receiver with a converter cable that has a mini phono-plug on one end and the red/white "RCA" plugs on the other. If you have installed a digital audio card and have a receiver with optical or coaxial inputs you can use the appropriate cable to get digital audio.
Once you've made the appropriate connections you should be able to treat the TV as a computer monitor and play your files with a software player like Media Player Classic or mplayer. You won't need to convert anything if you have the
right codecs installed.