What You Need
To connect a PlayStation 2 to an HDTV, you will need a component video cable. Most PlayStation 2s come with a cable that contains a yellow composite video cable and a red and a white audio cable. You will need to buy a new cable (available inexpensively in most game stores) that has three video cables (red, blue and green) in addition to audio cables. Before buying the cable, read the packaging carefully to make sure that it will work with your PlayStation 2 and TV. Some cables may be designed to work for multiple consoles or multiple video formats and thus may have a large number of plugs, but, as long as the plugs you need are there, you will be fine.
Connecting the Wires
One end of the cable should fit into one of the ports on the back of the PlayStation 2 console, just as the cable you are currently using. Connect the audio plugs into your TV just as you did with your old cable, matching the red plug to the red port and the white plug to the white port. Now look for three ports on your TV that are red, green and blue (they may be labeled as component video ports). Plug the three video cables into the matching ports on your TV, matching the colors. You should now be able to turn on your PlayStation 2 and have it work with the TV.
Configuring the PlayStation 2
Your PlayStation 2 games will probably look significantly nicer just as a result of changing the cable, but it is possible to get an even larger improvement. Go to the PlayStation 2 menu (by starting the console without a game or DVD in the disk drive) and go to the options menu. There you can enable progressive scan mode and change the screen aspect ratio, both of which should improve your system's graphics. Some PlayStation 2 games (especially newer ones) may also have a progressive scan option in the game options menu. Enable that as well.