USB Flash Drive
This is by far the easiest way to backup your data as long as you have less than 2GB or 8GB of data to backup. USB flash drives are getting bigger and cheaper so these numbers will always grow. But right now the flash drives between 2GB and 8GB are relativly cheap. The USB flash drive (or usb key as some call it) simply plugs into any open USB port on your pc and the drive will appear as a new drive letter in Windows Explorer. You simply copy the data you want to back up to the drive. You can then store the USB key in safe place for when its needed again to backup new files or restore something you lost.
External USB Hard Drive
This is another relativly easy option. External USB drives are also getting bigger and cheaper by the day. For example I just picked up a 500GB drive for $89. Most current home pcs dont have drives that large so a 500GB drive is more than enough to backup data. These drives also plug into any open USB port on your pc and appear as a new drive letter in Windows Explorer. This type of drive also has the benefit of automatic backups. Depending on the type of drive you purchase, many come with software that will automatically schedule and run backups so there is no user interaction. Many also come with a "One Touch" button that will back up everything on your pc with a single button press.
Install second internal hard drive in pc.
This option is a bit more advanced and requires you to open up your pc case and install a second internal hard drive. While this usually results in the fastest backups (time wise) it does not give you the benefit of easily removing the drive and storing it away from your pc in case of flood, fire or other damage to your pc. These drives are also relativly cheap and very fast but for the average home user I generally dont recommend this option.
Burn to CD/DVD
Most (if not all) new pcs and laptop now adays come with some type of disc writer, usually a DVD writer but occassionly I see CD burners. A CD will hold about 700MB and DVD around six times a much at 4.7GB. If your pc came with a CD or DVD writer then most likley it will have some software that will actually burn your data to disc. If it doesn't then Windows has a built in program that works but it lacks many of the advanced feature of other programs. There are also free download available that work very well for burning disks. InfraRecorder comes to mind. See my other posts about best free software for more details on programs.
Online backup solutions
Another option to backup your files and data is to have an online company store your files. There are several advantages and disadvantages to this type of backup. Many online backup companies offer some type of free plan that will give you 2-5GB of storage space. This may be ok if you are only storing word processing or spreadsheets with not many pics or videos. I usually find that videos and pictures take up a large majority of disk space on many of my clients home pcs. Even my wife has stored over 200GB of pics and videos. The online backup companies usually have service plans that will allow for more data but you will have to pay a monthy/yearly cost. This sometime turns people away from this option. For more info search google for "online storage".
Copy to another machine on your home network
Many families with kids these days have more than one computer. In most cases these computers are set up to all connect to the internet through a router (Linksys, Dlink, Netgear etc...). These pcs are connected to your home network. In the event that you have multiple pcs you can set up folder sharing on each pc and then copy files from PC 1 to PC 2 and vice versa. This option will not give you the ability to remove your data and store it but at least your data will be stored off of the machine in case of drive failure. If the pcs are far enough apart in your home then you can still get the protection from a flood, fire or other type of disaster. This type of backup job can also be automated if required. I will not go into the details on how to set up folder sharing as it is out of the scope of this article but if you would like more info please post a comment.
This one may be hardest of the backup methods as it requires you to have a tape drive connected or installed in your machine. As most pcs do not come with tape drive (or the software that backs up the data), this option is for more advanced pc users. Windows does have a small program called Windows Backup that will create a backup file and write to either a tape or folder location but there are far better programs for backup.