The course card appears on the Online courses main page when the course starting and ending dates are given in the course settings and the course visibility is set to "Show". 
NB! The course appears in the listing exactly that day and time which is set in the settings. So you can't "advertise" your course in advance on the main page. In the example below the course appears in the listing at midnight when the date changes to January 16th and it disappears late at night on the last of July.
Both dates are obligatory for the course to appear on the list.

This is how you do it: 

1. Give the course start and end date (and time) and choose Show for the course visibility.
Go to Settings > General:

2. If you want a certain image for the course on the listing, you have to add it in the course settings. If you there is no image added Online courses uses a default image for your course.

Go to Settings > Description > Course image. 

Add the image from the File icon or drag it to the area. Remember to save the settings.

The recommended picture ratio is 2:3 (height:width). If the original ratio is something else the image is cropped automatically to 2:3.