I'm going to make some assumptions, and let me know if this hits the mark.
1) Your DVD player doesn't have HDMI, but it does have component video. This is a set of three RCA plugs (Red/Green/Blue) for video and a set of two RCA plugs (Red/White) for audio.
2) Your TV supports component input - it has a matching set.
If this is the case, all you'll need to do is get a set of cables for component video and audio, and you're good to go. Don't get suckered by high cost on this. I haven't seen any difference in picture between the higher cost cables and the lower cost ones.
3) Your TV has a menu option (or maybe a button on the remote control) to switch the input it is using - either HDMI or component. If this is the case, wire everything together, and when you want to switch between DVD and cable, just switch the input that your TV is using.
If your TV or DVD player doesn't have component connectors, or if your TV is limited to only one HDMI input, then things will get a bit more involved, but just a bit. You can buy various connectors and switchboxes to make the connections work and automate the switching between devices, but let me know if the above helps before we set out to over-engineer your solution!