Backing up your digital images is relatively inexpensive these days with the advent of high quality archival CD's and inexpensive CD recorders often called burners. Even if your computer or laptop does not have a built in burner, there are many low cost external models that work with your computers USB ports. USB 2.0 devices are much faster than USB 1.0 devices - just make sure your computer supports the faster USB 2.0 standard before making your purchase.
Once you have your burner, you need to purchase a quality archival CD media to make your backups on. The key word here is archival as many CD's are available for purchase with many levels of quality. Four dyes are used in the manufacture of CD's two of which are commonly available. The first is a bluish dye that is commonly found in bargain spindles and other inexpensive CD's. This dye is not chemically inert and breaks down with light exposure and time. When you buy an inexpensive $15.00 spindle of 100 CD's, they may have a life expectancy of just 5 years even shorter if left out in bright light.
Always hold the CD up to the light before burning to check for any pinholes or other obvious damage to the media.
Even an archival CD is only one good scratch away from becoming a coaster. For this reason I suggest making two copies of important once in a lifetime images.
If possible keep your backups in a location separate from your computer. Some of our pro's go so far as to keep a second copy in a safe deposit box. If you are using a home fire safe be sure they are "fire rated" for CD media not just paper documents.
Save your files in a common file format. Once saved you need to keep alert to changes in formats and computer technology. The day you here talk about discontinuing CD drives is the day you should start migrating your backups to a new platform. Just think how hard it would be to find a 5 1/2" floppy disk today!
To be safe, plan on recopying your CD & DVD backup every 5 years or so. Store your disks in the dard or at the very least out of direct light.