I have tried unsuccessfully to save a character in the Ultima II game so that I can go back to it when my character dies. It seems that the saved character gets overwritten as I continue playing, and when I restart the game after dieing, I am back to tjhe same miserable state as I was just before dieing. How can I get the Save feature to work correctly.

The game auto-saves whenever you enter a town or dungeon, if that's what you're referring to. That can be overriden using the Ultima II upgrade patch, which you can find a link to in the Ultima resource collection sticky thread found here.

I downloaded the patch and put it in my Ultima II directory as instructed, But when I try to run the patch app, it says the program is not compatible with my version of Windows, What version does the patch app need?

If you try to manually patch the game, you'll have to do so inside DOSBox. The patch is incompatible with newer versions of Windows (64-bit versions). I'd suggest you use Pix's Ultima Patcher found under General Patches/Downloads in the same sticky thread here.