Obviously, staying up to date with everything on Facebook is now more important than ever. The simple and tested solution is to just have one tab always open on Facebook, though more advanced users could go for something like Facebook Messenger for Windows or Firefox.
But even with Facebook always open, there's still the problem of having to go to other tabs, or turn your eyes from the computer screen.
Facebook has a solution for this now, though it's still in testing. It is using a sound every time you receive a notification. It's still ironing out the details and only a few people have the feature, but it's encouraging.
With sound notifications, you'll know the instant you get a new like or comment. If you're lucky enough to get the experimental feature but for some reason want to turn it off, you can do that, just go to account settings > notifications > View and uncheck "Play a sound when each new notification is received."