how to back up my macbook pro to my external LACIE?

See instructions in Back up your Mac with Time Machine - Apple Support

Sorry for the delay, had so much going on at home & work now that the economy has opened back up.

Here is a screenshot (took me a google search to figure that out) of what I found when I open disk utility for that drive.

What is the next step?

You can not have anything you care about on the backup drive to start. if you do, it will be removed in the process.

Connect the drive to your MacBook Pro using appropriate cabling. In most cases, Time Machine control panel will open and ask if you want to create a new backup on this drive.

If not, open:

System Preferences > Time Machine ...

... and select the drive as a backup destination.

If you say OK, it will invoke Disk Utility and invite you to completely ERASE the drive by its immutable Device-name. Erasing only the Volume will NOT suffice. default should be MacOS extended (journaled) and NOT APFS. Choose a meaningful mnemonic name for the Volume. Completes in about a minute.

system preference > Time machine ...

turn it on and backup now.

By design, Time Machine is built into the system. It has access to everything. It does all its work at low priority in the background, so as not to interfere with your other important work.

But this means the initial backup takes ... all afternoon while it calculates what must be copied. Then several hours to actually copy the stuff.

The second and subsequent backups occur automatically, in the background, and you will barely know it is running.

NB>> Time machine copies MacOS Volumes. It Does NOT copy Windows Volumes, unless your Windows volume is simulated inside a MacOS file.

I did all of this up to the point of the erase process, and it stopped & now will not recognize the new disk when I go back into time machine even though it is plugged in. How can I rectify this? I have a brand new LaCie 5TB rugged usb-c that I have plugged into one of the regular usb ports as I have thunderbolt 2 on my mac (late 2012 iMac 27"). Any thoughts on what to do next? I've spend good money on this drive & can't use it!

At this point, I am not sure. I remember it saying it needs to erase the drive in order to use it for back-ups and I clicked OK and shortly after it seemed like it stopped whatever it is doing and is not showing up in the time machine settings as an option even though when I click on the apple logo to look at "about this mac", it shows this drive under storage there but nowhere else even though it is plugged into the usb port. I have restarted my mac several times & it's only viewable in the about this mac but nowhere else. I am not what you would call "proficient" in Mac as far as settings, etc. We are an apple family & wanted it for the compatibility & reliability. Otherwise I'm your basic computer user, if that helps to understand my knowledge of these things. Prior to this we had a time capsule that failed & I was replacing that with this LaCie drive for back ups.

Launch Disk Utility and select the drive by immutable device-name.

Post a screenshot.

I found it, thanks for your patience!

Did you erase it by Volume (which is changeable) or did you erase it by immutable device-name? You must choose to View by devices to see the device-name.

disk3s2 is an internal OS name, because you have selected Volumes in the view menu in the upper left of that pane.

Choose Devices from that menu, and post the pane with the immutable device name.

What is the next step?

I searched how to correctly erase & format to Mac for time machine. I am all good now.

Thanks for you help!