I am looking for cheap Asian producers that can make different plastic elements.
I am mainly looking for someone who can produce a large amount of thin
plastic plates with different shapes and measurements.

I also wonder how you approach to find information about factories in Asia.

I need this information for a business idea I have, and my main
problem is to actually find someone who can produce my product.

Thanks  JT

Try a search on www.asianproducts.com - a Taiwanese source of supply;
here you can also post your research; a lot of Taiwanese and Chinese
companies are reading the enquiries.