This is an image post format. Just set a featured image like you would normally do and the theme displays it accordingly.
This is a gallery post format. Just select the gallery post format, add images to the post and a default WordPress [gallery] shortcode.
Edge is an incredible theme, this is your new site, you just don’t know it yet!
This is a quote post format. Just select the quote post format and add a [blockquote] shortcode.
This is a video post format. Just select the video post format and use the [video] shortcode to display it.