AcyMailing

How did I aktivate my AcyMailing please? I can't find out to get started with it

You need to install AcyMailing first:
www.acyba.com/en/support/documentation/6...mailing.html#install

You can download it here:
www.acyba.com/en/download.html

I thought that AcyMailing was in the Business Package. Do I have to by it first?

The plugin to integrate with AcyMailing, yes.
AcyMailing itself needs to be downloaded separately on that page:
www.acyba.com/en/download.html
Then, you can install it on your website.