You dont't have to use paper. Cardboard, plastic sheets, even metal would work.
Any cast starts with a mold. You need something to pour your material into, be it concrete, plaster, resin, wax, whatever. You can user everyday objects like bowls, packaging or make molds from existing objects.
But what if you want cast something completely different? Something you can't make casts of?
Paper to the rescue. Everyone has some lying around, has scissors and glue. And paper can take pretty much any form you want.
It does have it's limitations though. It's not waterproof and will lose it's strength when getting wet. So before you can use it as a mold, you'll have to make it waterproof. I'll just use spraypaint. Also it's strength is limited. So making huge casts doesn't work. The "Venus de Milo" is 36cm (14 inch) high - and it worked out just fine.
Paper is great to work with, it's easy to cut, fold and glue. But if you want to make more than one cast of your mold you might want to try sheets of plastic. While it is a lot harder to work with it is reusable. You can make many casts with the same mold over and over.
Here are two different routes I took
Step 1: The "gothic" Vase
This is the last one I made and it's the one I documented best.
It's a cast made from David Huffmans "Hexagonal column with cusps". I took the blueprint from the following paper by Erik and Martin Demain and Duks Koschitz.
There is a tutorial on youtube on how to fold it: