I have a camera with a USB port when I connect it to my laptop I see everything the camera sees?

There was a CD that I had to play on the laptop but now I have a new laptop without a CD drive so you can't put a CD in there. How can I use the camera there?

You download the current software version from the manufacturer's website and install it.

So theoretically like on the old laptop with the CD only without CD

Yes. What about downloading (from the internet) did you not understand?