Really depends on how much your willing to spend.
You could get another drive identical to what you have, and put it in RAID1 with the one you have. That means if there is a drive failure, you still have all of your data.
Note: This isn't really a backup, you can still lose your data through human error, software means like a virus or in some event that takes out both drives (power surge, fire, etc). It only protects against drive failure.
However much your HDD costs.
Another option is too get an external HDD, copy over everything valuable on your PC to it and keep it somewhere safe. Even if the whole PC blows up, you still have everything important on your external drive. You will need to copy over everything manually, the capacity of the drive will be a limiting factor in how much you can backup and the frequency you backup your data will dictate how old whats on the drive will be. If your working on a paper and everything goes down, your back to the point you were whenever you last backed it up.
$100 or more depending on the capacity of external drive.
Backing up to the cloud is a similar option, though will have some more automation features. It can be expensive and will be even more time consuming to upload the data to the internet. On the plus side, your whole house can blow up and you still have the data.
Depends on what service you get.
The next option would be a NAS or a backup server. Its basically a PC with storage space connected to yours by your home network, and you can backup all your data to it through the network. Should be easy to setup automatic backups.
If your computer blows up, everything should be on the NAS and it will up-to-date by a day or two.
$300 for the PC (if you have an older PC, you can use that), then add storage (which can be a lot depending on how much capacity and redundancy you want). Assuming your home network is up to it.
You can also use the NAS as a general storage area for anyone on the network, removes the need for large amounts of local storage.