How can I clean my interior?

[Dennis Jones]

My car is a 1933 Master 5 window coupe. It was probably restored about 40 years ago. The interior is old and not in great shape. I am afraid of destroying it trying to clean it, and I can't really afford to replace the interior at this time. I am not even sure what kind of material it is. Here is a short video of it.
I'm open to all suggestions. This forum has helped me figure things out many times and I am thankful.  

Thanks,

Dennis