Backup your files? You should have an external hard drive for that. You can simply plug that in to your Mac, and your Time Machine software should (normally) ask if you want to use that external hard drive for a Time Machine backup. Or, you can open your System Preferences/Time Machine, and turn Time Machine ON, (you may have turned it off at some earlier time), and let Time Machine take care of your backup. The backup will likely take several hours.
There's other software options for backups, such as Carbon Copy Cloner, or SuperDuper!
This might also be a good time to consider upgrading/replacing your hard drive with a larger capacity...
How large is your hard drive now?
If you Get Info on your hard drive, you can see the capacity, and how much free space you have left (among other items.)
You will get a low space warning when free space dips below about 200 MB. You may also see that low space warning, even if you have more space.
Most experienced OS X users will tell you that you should keep at least 10% of total capacity as free space, and some even suggest up to 25% free. In these days with possible TeraBytes available, I'm not sure if you would ever need to keep 1 TB free on a 4 TB drive, even if a boot system - but more space is better.
You can also sometimes recover a lot of space by removing old log files, and various system and user cache files. There's good utilities that can make a cleanup of those various temp files very easy - such as OnyX, or YASU.