How can we free disk space by removing unwanted data on the system? How do we detect that the files are not necessary for the programs to work?
You can use "diskspace analyzer" to see what is using space. It is installed by default. You should not delete things outside of your home directory unless you know what you're doing. Before you delete things, it is a good idea to rename them to see if everything still works. When you know that it does, then you can safely delete them.
I also recommend the same as Jo-Erlend but there is also a little bit of cleaning with the download packages that you already have installed.
For example with the command
You also have the tool Ubuntu-Tweak:
Then run ubuntu-tweak. It has an option for cleaning up called Janitor:
Lastly you have Bleachbit (Or ChlorineByte ^^) which has several FEATURES which include cleaning the cache from Firefox, Temp files for more than 50 programs and other stuff that is mentioned in the Features page.
The Software Center comes with version 0.8.8 and the Official Page has the 0.9. Whichever you use will do the trick since the difference between version is SMALL.