I believe you are simply looking for the “read more” button located in the editor.
When you are creating your post/page, choose the location where you would like the “break” to occur, and click the “read more” button in the editor. If you don’t know which button it is, you can mouse over each one looking at it’s popup tooltip.
Once you’ve clicked the button, you will notice a code that looks like this:
<!-- read more -->
Now, save, and view your home page. You should see the content up to the point where you inserted the read more link.