How to save files from MacBook Pro to External Hard drive

Hello. I'm a new Mac user, and I have no idea how to work this thing.

I am able to view files from the external hard drive, but when I drag the files I want to save to the external hard drive folder, it won't let me and shows the stop sign (or whatever it is). Do I have to allow a connection or?

How can I save files to the external hard drive because my Mac is full on space, already.