When dealing with a malware-infected system, the first step is to isolate and remove the malware before proceeding with data backup. Once the malware has been eradicated or quarantined using reliable antivirus software, data can be backed up using various methods, such as copying files to an external storage device, creating a backup image using backup software, or utilizing cloud-based storage services. It is crucial to ensure that the backup is performed in a clean and secure environment to prevent the transfer of malware-infected files.