If you have just purchased your first HDTV, you will want to do some research on what cables to use when connecting your hd tv to your dvd player.
Most likely, your old DVD player was connected to your old TV via a composite video cable or an s-video cable. You can use these cables to connect your DVD player to your new HDTV, however you will not achieve the highest quality.
Many DVD players have a component cable-out connection that you probably didn't use or weren't able to use with your old tube TV. It is a cable with 3 video cables (red, blue, and green) instead of one yellow cable.
Using this component cable with give you a significantly higher quality picture that will look great on your new hdtv.
Another less common option is an HDMI cable. Some higher quality DVD players have this connection. If it is available, use it. It offers the highest quality and passes both video and audio signals though a single cable.
Most of these cables can be purchased for a relatively low cost at a local store or on the internet (be careful.......some places can charge in excess of $100 for HDMI cables that are probably more expensive than you need). Its a great way to get a picture quality upgrade with very little effot.