Go to Pages, Add new Page an create it with whatever you want: images, text, reusable text etc.
Publish it , write an excerpt.
OR Simply use a Page you have already produced
Go to Appearances then select Widgets. Choose type of widget eg Text.
Select where to put it eg Main Sidebar
Then Add Widget and put in Title, and a brief Introduction
Next put in the link to the page: Click on Text and select Link
From the list of pages that appear click on the page you want. The link then goes into the link slot.
Save and close.
When you go to the Home page the widget should be there and should link to the article.