how do I back up my computer before service today

The most common way is to attach an external drive and use Time Machine. See information in: Back up your Mac with Time Machine - Apple Support

Having a backup is advisable all of the time, not just when having service done.

Firstly, I want to say you're making the correct decision in trying to back up your Mac. It's always important to do this before any update or in your case service. :) - I know how horrible it is to lose data and I want to make sure everything is good to go for you!

This link will help you out :)

How to back up your Mac - Official Apple Support

Open Applications/Utilities/Disk Utility, select the disk, and click the Erase Button in the menu bar.