Welcome to the IPFire Community.
When you make your backup, select the Include Logfiles option at the top of the WUI backup page. This saves all the logs as well. The backup file will be larger.
Then select the yellow symbol to the right of the backup(s) that you want to save. This is the Download button. The Green one is the Delete button. If you put your mouse over the icon the usage for it will be displayed without having to press it.
When you select the Download icon it will open a file window where you can select where you want to save it to on the PC that you are browsing from. Download as many as you want but ensure you download the one created with the logs. If you have any addons and they have backups then do the same with them.
After installing IPFire from scratch then go to the Backup WUI page again and go to the bottom where the restor section is. Select Browse and choose the backup you want to restore from. This should be the one you have done with the logs. Select Open and it will select it on the WUI Restore section. No File Selected will be changed to the file name. Then press the disk icon at the right. This is the Restore button. It will then restore from the backup you selected.
Then install any addons you used to have (make a list before you re-install if there are many)and then restore the addon backups with the same process as used for the Core backup.