How do I make my external hard drive work on my MacBook Pro?

Have you formatted it Mac OS Extended (Journaled) GUID Partition Scheme. If that's correct, then you should be able to plug it in and see it on your Desktop. If it's not there then go to Finder menu > Preferences > General > "Show these items on the Desktop" and check mark "Hard drives"

Glad you got it mounted. Looks like it is a TIme Machine backup. The way to access a Time Machine backup is to open the Time Machine interface from the TIme Machine app in your Applications folder. You should then be able to view your individual backups and files. Then you can restore files from there.

Restore items backed up with Time Machine on Mac - Apple Support

It's possible it has to do with the power outage, did it work previously? And did you try mounting it from within Disk Utility?

Here's another way you can try to mount it:

Launch/Utilities/Terminal and copy & paste this command at the prompt:

mount /dev/disk3s2

Press Return.

Also might try

mount force /dev/(number of disk)

OK but it should be simple. When you plug it in just launch Disk Utility from your Utilities folder. And it should be listed there?

OK well at least it sees it, so we know it's connected. Can you choose it in Disk Utility and click on the Mount button?