1) To abbreviate a post on the main page, you use the more tag:
2) A post slider is an optional section (below the header) that showcases selected posts in the form of a carousel slideshow. Check the Sundance demo:
3) In Sundance, a post will show up in the carousel if you've marked it as a sticky (post editor: Visibility module) and if you have selected the Video post format for it (post editor: Format* module).
4) You don't have to post videos for the carousel to work. But since the Sundance carousel is primarily designed for video posts, it has two columns: left column for video (or image), right column for description. The description is entered in the Excerpt* module of the post editor.
*If you're not seeing the Format and Excerpt modules while on the post editor screen, click Screen Options (top right) to activate them.
If you publish a regular post (text only, or text and images) and set it as explained in 3 above, the carousel in Sundance will display the complete post in the left column (or part of it, if you use the more tag) and the beginning of the post in the right column, which doesn't make sense. So you must either a) start your carousel posts with a large image, use the more tag after it, and enter the beginning of the text or a custom summary in the Excerpt module, or b) start your carousel posts with text, use the more tag at some point, and copypaste the code of an image from the HTML post editor into the Excerpt module.
That's an unnecessary complication if you're not interested in video or image posts. So if you really want a post slider on your main page you could try a different theme. Themes that support a post slider listed here (marked with ***):