See that Facebook tab on the right hand side of my page. You can have one too!
I recommend either of the following two WordPress plugins. They pop out or slide out to display the Facebook Like Box when you click on the tab (or you can set them to slide out on hover). Then you simply click on them to slide back in. Plus they can be disabled on tablets and mobiles if you wish so the tab doesn’t take up too much of the small screen.
Be-It Facebook Side Tab
This is the one used on my site. It has a number of display options you can even change the tab image (I’m using the default). Although the plugin hasn’t been updated for a while, I only recently installed it and it works a treat.