Firstly, you need to connect the DVD to the tv using an HDMI cord. If it's older it won't have this (only scart) or seperate analogue cord such as red/white/yellow.
So if it is an older player without HDMI, you should replace the device with a bluray player. You can then connect with HDMI, and adjust the resolution output of the player to 1080p (full HD) and enable 24fps if it has that. Not forgetting switching it to widescreen 16x9 mode. This should give the best results on DVD and Blu-ray Discs.
In general, DVD is SD quality - just like one of the regular live to channels (not the HD versions). Actually the data capacity on DVD is quite good so pre-recorded DVD pictures should look a bit better than regular sd tv channels. With this in mind, how bad do those regular sd tv channels look on the new tv. If you get similar poor results with those it may simply be that the tv manufacturer has cut costs by putting in a really cheap, poor scaler (on the assumption that most things are now in HD quality via live tv and bluray).