I have a full-volume backup in a folder or a disk image, but I don't have a bootable backup. How can I restore everything?

CCC makes bootable backups specifically to avoid this kind of situation. When you have a bootable backup, you simply boot from that, then restore everything to a replacement disk or the original disk. One step, minimal time, couldn't be easier. Occasionally people get into this sticky situation though -- I have a backup of everything in a disk image or in a folder on the backup volume, there's a clean installation of macOS on my replacement disk, now how do I get everything back to the way that it was before?

The first thing that you need to do is make a boot volume that is not the volume you want to restore to. Once you have done that, you can boot from that volume and then do a complete restore of your backup to the replacement disk. There are several options for how and where you create this other bootable volume. For example, you could install macOS onto a thumb drive, or you could use CCC to clone your clean installation of macOS to a thumb drive. You could also create a new partition on your replacement disk and clone the fresh installation of macOS to that. The steps below attempt to make very few assumptions about the resources you'll have in this scenario: a) You have a fresh installation of macOS on a hard drive and b) you have your backup in a folder or disk image on some other disk. Given those assumptions, here is how we recommend that you proceed.

Create a new partition on your replacement disk

1. Open the Disk Utility application and click on the disk icon that represents your internal hard drive. Don't click on the Macintosh HD icon, click on the one above that.
2. Click on the Partition tab.
3. Click on the + button.
4. Set the size of the new partition to 15GB and name it something like Rescue.
5. Click the Apply button.

This video describes the same procedure (albeit in a slightly different context).

Clone your fresh installation of macOS to the Rescue volume

1. Open Carbon Copy Cloner and create a new task.
2. Choose your current startup disk as the source.
3. Choose the Rescue volume as the destination.
4. If you aren't working from a fresh installation of macOS, choose Selected files... from the Clone popup menu and take a moment to exclude third-party applications from the list of items to be copied, as well as any large items in your home folder (e.g. /Users/yourname/Music).
5. Click the Clone button.

Boot from the Rescue volume and restore your data to the replacement disk

1. Open the Startup Disk Preference Pane, set the Rescue volume as the startup disk, then click on the Restart button.
2. Once restarted from the Rescue volume, attach the backup volume to your Mac and open the Carbon Copy Cloner application.
3. If your data is backed up in a folder, choose Choose a folder... from the Source selector and select that folder as the source. Otherwise, choose Restore from a disk image... and locate your backup disk image.
4. Choose your Macintosh HD volume as the destination.
5. Verify that CCC's SafetyNet feature is enabled.
6. Click the Clone button.

Reboot from your restored volume and clean up

1. Open the Startup Disk Preference Pane, set the restored volume as the startup disk, then click on the Restart button.
2. Open the Disk Utility application and click on the disk icon that represents your internal hard drive.
3. Click on the Partition tab.
4. Click on the Rescue volume, then click on the - button to delete that volume.
5. Click the Apply button.

Finally, make a new backup to the root of a locally-attached hard drive so you'll have a bootable backup from here forward.