Each article will have properties such as the title, date, authors name and Introtext. The introtext is the main article text that you have before the cut off. The cut off comes from the "Readmore" button/link.

In article manager, create a new article. If you have a section and category for your blog or news, choose them. Write the entire article in the editor. After the text and images (if any) are entered, place your cursor where you want the introtext to be and the rest of the article cut off. Now click the "Readmore" or sometimes just "More" button at the bottom of the editor

Now visit the frontend of your site and visit the blog or news page. Only the text before you put the "Readmore" button should show.

Sometimes the "Readmore" button can be a little buggy depending on what editor you are using. If it's not working, try to view the article in the html editor and do the same thing, place the cursor where you want and click "readmore". See if that helps.