Of course, archiving and data storage are very important to most business and there is a huger market for providing those services. While these solutions are overkill for the home, they can provide good examples of how it should be done.
If your personal data is important enough to archive, it is important to insure that the backup will always be available and be free of corruption. Therefore, you should:
1. Have multiple copies of your dataThe kind of data you want to archive can help in the decision of how best to archive it. For example, family photos would be data that would suggest multiple backups for protection against loss, but not on media that would be accessed every day. Your work for the day might best be kept on a single local external hard drive in case your personal computer fails. Important work might be archived remotely to preserve it in the case of a fire or flood or surprise nuclear attack.
2. Keep copies in multiple safe locations
3. Always test your backups
The most traditional method for home backups and storage is to use CDs or DVDs. The big benefit is cost (relatively cheap) and the big drawback is limited space per disc and the fact that DVDs and CDs will degrade over time. It can also be time-consuming to back up large amounts of data, so that backup task is often "forgotten" over time.
There is a newcomer to the scene, M-Discs. Very durable and available in a 4.4BG DVD and 25GB and 50GB capacities. They do require a special drive, but these are surprisingly affordable and can access all of you old Cds and DVDs. It does take a long time to burn a 25GB disc, so that should be considered. And remember that you will need a stack of these discs to back up the multi-terabyte drives that are now affordable.
External drives are popular choices and multi-terabyte capacities are available at reasonable costs. Making backups if much faster than burning Discs, but mechanical hard drives can and do fail, often with no warning, so multiple drives at different locations kept in sync is a good idea. A good strategy is to replace the drive when it reaches its MTBF. An app named Delta Copy can keep files backed up in real time to a local drive or a remote drive, but not both.
Online archive storage site, commonly known at "The Cloud" is popular. This page provides some details about each service and the availability of "free" storage. If your needs are greater than the "free" storage capacity, you can pay to add more or simply use more than one service. Note that Google also offers storage as a component of its many services.
An additional option, often not considered, is to create your own "cloud" storage. This is accomplished by installing Nextcloud software on a computer you own, turning it into a private "cloud". There are some drawbacks to this that present some serious concerns. The hardware may fail, the computer itself may become damaged by flood or fire or it may be beyond your skill-set to configure such a device.
Finally, no storage solution is useful if you cannot restore your files from it. It makes sense not only to practice doing that, but to practice doing it on a regular basis.
Data backup, like home insurance, is often insufficient when you actually need to use it, but something is better than nothing.