I have a old "cable ready" TV and a new vcr/dvd player.
There is only a cable connection on the TV and multiple connects
On the dvd player. I can not seem to connect anything. Do
I need some kind of adapter and if so what kind? If it matters,
I do not have cable TV service.

Your need this RadioShack.com - Home Entertainment: Accessories: Video accessories: Converters: RF Modulator

I have used this type of product before, works good. You can use the Radio Shack version or another electronics retailer should have it locally.