External Hard Disk Drive
This might be the most common and easier way, make sure the hard disk is double the size the computer you want to backup since your backup will be growing over time and as days go on they might contain backup from other sources. Make sure your backup are not kept on the same location as your computer. Imagine someone steal your laptop and backup at a go, or what about the natural disaster eg. Fire, flood.
Backup on the cloud
Cloud backup is very common nowadays, there are many companies providing cloud backup services. I have been using a number of these services. The most common cloud service that I have tested myself are Dropbox, SkyDrive and Google Drive. They all have free space and paid version. You can divide your files and back them up on separate services if you have many files that exceed the storage they are providing, but you can decide to purchase the paid service. What if you wake up in the morning and find that you do not have access to your cloud service? Always keep three copies of your important files.
Partition your Hard Disk
You can partition your hard disk and have two logical hard disk drive eg. Drive C and Drive D and keep a copy of your data on a separate drive from the one that has operating system. I do not consider this method a backup because your files will still be susceptible to viruses since they are in the same computer with the original files and if a natural disaster occur you lose everything. This method will help you when the operating system crashes.
You can choose to backup your data on the DVD or on the CD, this method might not give you the flexibility of adding files to your backup but it is very effective if you have files that do not require updating so often and they are very handy on moving them to the offsite location.
Do not rely on one method, all your important data should be backed up using three different methods. I did not mention having a server and make backup to the server as this article is focusing on end user/none technical personnel. With all these methods consider offsite backup. and most important test your backup, imagine the situation whereby your computer has crashed and your backup is not working. When you have backup of your important data do not forget to backup your phone too.