As an example, this little guide demonstrates how to change the icon of Kate, an excellent text editor. Why Kate? Because its icon is ugly, in my opinion. Of course, this is applicable to any other application. This assumes you’re using KDE Plasma, where Kate is the default text editor, but it will probably work on most other DEs.
The procedure is simple:
Copy the following .desktop file:
cp /usr/share/applications/org.kde.kate.desktop ~/.local/share/applications
You might have to mkdir ~/.local/share/applications if cp fails if that directory does not exist.
Open it with a text editor of your choice (Kate, for example):
kate ~/.local/share/applications/org.kde.kate.desktop
Find the line that says:
Icon=kate
And change it to:
Icon=accessories-text-editor
Save the file, and just like that, the monstrosity is no more the icon is changed! 
To undo the change, just delete the newly created file:
rm ~/.local/share/applications/org.kde.kate.desktop
Of course, you can experiment with other icons, and with other applications. Any .desktop file that is in ~/.local/share/applications/ will take precedence over the one in /usr/share/applications/. This should also be update-proof, as updates should not touch your home directory.
I forgot that .local entries should override 