Probably depends on where the full story is written.
If it's written on a blog page (which I would probably recommend as it makes a lot of stuff simply easier to edit for just the stories) you can use the Read More Break component to make it so that the previews only show up to the point you want to show (in your case a few lines) and to read the full story they will be forced to press Read more to open the full article.
Example taken from: https://www.powershellder.com/blog
If the stories are written within text blocks on a normal page though, which probably isnt the best idea if you're intending to have a lot of stories on the website, the only way to do it would probably be to copy the first few lines and then have a link to another page on your website where the full story is.
