If you download and use the Minimum Child Theme you will have to change the image using FTP. Create an image called sample.jpg and upload it to the images sub-folder under theme folder on the server. You would use FileZilla or some other FTP program to do that.
However if you've used Whoosh to whoosh any of our Mimimum theme variations, then the WordPress install will come with a plugin called the Genesis Club plugin. This plugin enables you to upload a new photo to the Minimum home page without using FTP.
The video explains how to do it.