How can I back up my files.  

First purchase a flash drive or an external hard drive.  If you have a lot of pictures get an external drive.  If you only a few hundred or even a few thousand get a flash drive.  Flash drive are more reliable because there are no moving parts.  

Use a program like Microsoft SyncToy that installs on your computer and will automatically sycn any new files to your external device.  You can set it up to run on a schedule or you can manually initiate it.  That will give you a local copy of your files and since it only backs up new or changed files, after the initial sync all future syncs will be fast.  If you try to do it yourself you have to figure out what you already copied and what hasn't been yet.

A local copy wont help you in case of a fire, burglary, ect.  What I use is a program called Mozy.  They offer both a paid version for $4.95/month with unlimited storage or a free version with a 2 gig limit.  See below for details and to sign up.  Its software that installs on your machine and you set the schedule when to backup.  I have mine set to backup any new files or changes every 2 nights at 9:00.  A high speed internet connection is needed and the initial backup may take some time but after that they are fairly quick.  To me $4.95/month is worth a piece of mind knowing all my pictures are backed up.