The old way was that the user would install Wolfram Player on his computer and then the browser would use Wolfram Player to show CDFs in the browser. There is a new way that can also show CDFs in the browser but instead of computing the result, the computation happens in the cloud. You can see an example of that here: https://www.wolfram.com/cdf/adopting-cdf/deploying-cdf/web-delivery-cloud.html

Here is a question about this here on Wolfram Community: https://community.wolfram.com/groups/-/m/t/834960

I have not tried this but the instructions given by Andre seem straightforward enough to follow.

Thank you Calle for your very informative answer.

If it's the case that cdf´s don't work, - then what is the best method to display interactive content (lets say Manipulate) on a WordPress site? If there is an alternative, could you give me some examples of sites that use the method in question.

Best regards

Math