How to delete unnecessary Fields in FileMaker

Export the Field/s to Excel and press Ctrl+Down. 

If the Field is empty it will go down all the way to the last Cell of the current Column. 

Now press Ctrl+Up and if the Field is empty it will go up all the way to the first Cell of the current Column (which is the Field Name). 

Continue with going down and up until you reach the last populated Column.
However if the Field is not empty then instead of hitting the bottom or the top of a Column it will stop at a Cell that contains some Data.
Highlight the Field to distinguish it from the other - Empty - Columns and do the same with all Columns containing Data.

Before continuing with this procedure,
it would make sense of course to back up the file, so that in case you make a mistake you will have the backup file to fall back on.

Now you're ready to delete the empty Fields in FileMaker: Ctrl+Select the Fields in Manage Database and hit the Delete button.