Backup to an external hard drive. This is probably the quickest, most cost effective option. You can often get a removable drive on sale or with rebate for a low price too. You can get one with hundreds of Gigabytes of space too. They can be easy to hookup to your notebook computer. However, do remember that they are hard drives and hard drives can fail. You may find the external backup fails before your notebook computer does.
Online backup. This is actually a good idea because physical disasters can happen to your home. And when that happens, you will always have a copy in a place not affected by the disaster. This is why businesses usually have one backup in the premises and one (or more) off premises. The good thing about online backup is, it's accessible from anywhere with an internet connection. So if your notebook fails when you're away from home, you can still retrieve your data.
Many of these services are reasonably priced and they provide you with everything you need to get the backups safely transfered. But because your data will be on someone else's system, choose a reputable company, one who is not only established but takes customer data confidentiality very seriously.
Network attached storage. This would make more sense if you have several computers. They allow you to not only backup several computers' data into one location but also ability to share or retrieve files from that central area. You can also achieve a similar effect equipping an older computer with a large hard drive and use it just for storage or backup.
Backup to CD or DVD. This is considered the safest for long term data integrity. External drives and network storage can still crash and prone to virusses. CD's and DVD's are also inexpensive. But backing up to disks daily is chore as you'll find yourself having to manually pop in the disks. It becomes even more hard work when you have a lot of files and your backup spans several disks. The other problem with this method is, backup utilities that come with your operating system cannot backup to a CD or DVD drive. So you'll have to fork out extra cash to buy a third party backup software that will.
No backup solution is one hundred percent and what you choose of course will depend on how you work. If your data is really important to you, try not rely on one backup source. Create two separate sources if you can afford to, just in case.
Lynn Chan helps new owners learn proper notebook care and use. Start taking care of your investment, with this free course 5 Days To A Healthier Notebook Computer