Thank you very much!
I just found the option in the control panel of my webhosting (Direct Admin) which me allows to define cron jobs. I created a cron job and defined it will send all the output to my email. When the cronjob completes the task, it sent me the message
After finetuning the email settings in webtrees I also received the first email with coming events.
Thanks a lot for your hint.
In the reminder module settings in webtrees I selected my name and one other user to receive a list of coming events. The other user has a user level Restricted to immediate family: 2.
These user didn't receive a mail today unless the level is set to "No". Why? Are there no coming events in the restricted family or is there another option I have to set?