Please ensure that your External drive is plugged in and mounted. If you can access it or see it present in your File Manager, then you know it is mounted.
You can then open the App menu and type
disks. Click the
Disks utility presented in the App Menu.
The Disk Utility will open giving you a Graphic of all disks currently mounted. Your primary drive, any usb drives, external drives, etc. Click on the rectangle representing the External Drive you wish to change permissions on.
Underneath that graphic is a list:
partition Type and Contents.
Device is the one you want to keep an eye on. When you select the External drive in the graphic, then Device will change to that Device I.D. It will look something like
/dev/sdb1 where sdXX can be the variable, depending on that particular device I.D.
You can now use that information in the terminal to change ownership to YOU.
In the following, change $USER to your actual username that you use accessing root and your computer. Change /dev/sdXX to the device I.D. you got from the Disk Utility, above.
Open terminal with ctrl+alt+t keyboard shortcut and enter into it the following, changing $USER and sdXX as outlined above:
sudo chown -R $USER:$USER /media/dev/sdXX
chown command is for Change Ownership. The
-R sets it recursively, so that it changes ownership in all files, not just the Top Directories. $USER:$USER is you and the /media/dev/sdXX is the path to the external drive.