Running the command df you get "command not found". What could be wrong and how to fix it?

Most likely the default/generated $PATH was somehow modified or overridden thus not containing /bin/ where df would normally go. This issue could also happen if bash_profile or any configuration file of your interpreter was wrongly modified, causing erratics behaviours. You would solve this by fixing your $PATH variable:

As to fix it there are several options:

1. Manually adding what you need to your $PATH PATH="$PATH":/user/bin:/..etc
2. You have your weird env variables backed up.
3. You would look for your distro default $PATH variable, copy paste using method #1

Note: There are many ways of getting errors like this: if bash_profile or any configuration file of your interpreter was wrongly modified; causing erratics behaviours, permissions issues, bad compiled software (if you compiled it by yourself)... there is no answer that will be true 100% of the time.