Most likely in the control panel of your account at your host there will be MySQL or something to control the database. When I click on it one of the options is manage backups. You should have something like that – ask your hosts how to back-up the db.
You can from that same control panel using the file manager, create a mirror image of the site in an alternate directory. One way to back up but not the best in case there is a problem with the server.
Look for ftp information on your control panel. Download and install FileZilla, https://codex.www.ads-software.com/Using_FileZilla. It will want the same info that in is your wp-config.php file to set up. Then use that as esmi said to ftp the files.
It is easy really and puts you in control of your backup not some stranger.
Do I really need to update to every new version of WP or can I run an older version for years?
Only if you want your site to stay up and not get hacked or loose functions.
