There are two ways to go about doing this.
- The McGuyver Way
Create a category called “Featured” then on the front page, simply call a post loop of the featured category. Old featured posts can be removed, or they can just fall off after they are no longer in the top 3-5 you are showing.
- The fancy pants way
Create a meta box option to feature the post, call that meta box as a checkable item in your admin list, replace the checkbox with a graphical check, then call the post loop based on the featured item meta key. The only advantage here is that you make it look a lot more natural in the GUI. If you don’t mind not having an interactive “featured” check box in the post list (you have to edit the page to change its status), you can set up a 90% solution using ACF and CodePress Admin Columns. I’ve actually requested interactive checkbox columns but they aren’t in the devloper’s immediate timeline.
From here, you should be able to grab the rest of the code with a couple of quick searches. Laying out how to create a meta box or display a loop by either category or key is really beyond the scope of the answer, since it’s specialized to your site.