How do I back up my iMac 21.5' late 2015?

Sorry for your loss ...

... Macs are typically backed up with an app called Time Machine (TM). These backups would be sent to either an external drive or an Apple Time Capsule. If he had been using TM, these would be the first place to look for backups if his computer is not currently accessible.

Apple can assist you with gaining access to his Apple ID. The following support article provides the steps required:

• How to request access to a deceased family member's Apple account - Apple Support

This would give you access to his iCloud account, and any data he stored there. However, it would not allow access to his computer.

Apple does not make device specific manuals. Only Operating System manuals which cover all devices that Os can be installed on.

click here ➜ macOS User Guide - Apple Support

Sorry for your loss.

To backup you can use Time Machine with an external drive. If the computer has an external drive connected to nearby it may have a backup, but the only way to know is to connect it the computer and see what's on it.

click here ➜ Back up your Mac with Time Machine - Apple Support

If you need to get access to your husband's Apple ID see the following support document.

click here ➜ How to request access to a deceased family member's Apple account - Apple Support

Here is the page from the manual on backing up:

Back up your files with Time Machine on Mac - Apple Support

Note that you would select the operating system you are using from the drop down menu.

Here is the main link to the manual:

macOS User Guide - Apple Support

You may also find this page useful:

iMac - Official Apple Support