Can you list directories with ls -l or du? These will show space used. If you can find a large file you do not need, you can free up space. Most file systems will have space reserved for "root". If you have used that up you may have to boot with SystemRescueCD and delete files from there.
It can happen that you run out of space as you are trying to add stuff to a PC. There is almost certainly a solution. The rm command will remove files you do not need. You may also be able to clear out the /tmp directory. Boot to "single" and clear it out. cd /tmp;rm -fr [a-z]* will remove all files and directories in /tmp starting with "a" to "z".
Look for old .iso or useless backups and .tar or .tgz files in /root or your /home/user directory. Delete unneeded accounts and their /home directories. Empty caches that may be stale. Some packaging systems keep the downloads. Empty them. In apt, apt-get clean does it. I have not used RPM for years but there is probably a similar option. You may also be able to delete old /var/log/files.
With updates there may be some old kernels hanging around. If you find one you know you do not need, uninstall it.